Join Professor Mary Pyo’s Geometry online class for time-saving lessons that include clear explanations of difficult topics and step-by-step examples. Special emphasis is placed on geometric proofs with insights and strategies taken from Professor Pyo’s 15+ years of teaching experience.

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I. Tools of Geometry

  Coordinate Plane 16:41
   Intro 0:00 
   The Coordinate System 0:12 
    Coordinate Plane: X-axis and Y-axis 0:15 
    Quadrants 1:02 
    Origin 2:00 
    Ordered Pair 2:17 
   Coordinate Plane 2:59 
    Example: Writing Coordinates 3:01 
   Coordinate Plane, cont. 4:15 
    Example: Graphing & Coordinate Plane 4:17 
    Collinear 5:58 
   Extra Example 1: Writing Coordinates & Quadrants 7:34 
   Extra Example 2: Quadrants 8:52 
   Extra Example 3: Graphing & Coordinate Plane 10:58 
   Extra Example 4: Collinear 12:50 
  Points, Lines and Planes 17:17
   Intro 0:00 
   Points 0:07 
    Definition and Example of Points 0:09 
   Lines 0:50 
    Definition and Example of Lines 0:51 
   Planes 2:59 
    Definition and Example of Planes 3:00 
   Drawing and Labeling 4:40 
    Example 1: Drawing and Labeling 4:41 
    Example 2: Drawing and Labeling 5:54 
    Example 3: Drawing and Labeling 6:41 
    Example 4: Drawing and Labeling 8:23 
   Extra Example 1: Points, Lines and Planes 10:19 
   Extra Example 2: Naming Figures 11:16 
   Extra Example 3: Points, Lines and Planes 12:35 
   Extra Example 4: Draw and Label 14:44 
  Measuring Segments 31:31
   Intro 0:00 
   Segments 0:06 
    Examples of Segments 0:08 
   Ruler Postulate 1:30 
    Ruler Postulate 1:31 
   Segment Addition Postulate 5:02 
    Example and Definition of Segment Addition Postulate 5:03 
   Segment Addition Postulate 8:01 
    Example 1: Segment Addition Postulate 8:04 
    Example 2: Segment Addition Postulate 11:15 
   Pythagorean Theorem 12:36 
    Definition of Pythagorean Theorem 12:37 
   Pythagorean Theorem, cont. 15:49 
    Example: Pythagorean Theorem 15:50 
   Distance Formula 16:48 
    Example and Definition of Distance Formula 16:49 
   Extra Example 1: Find Each Measure 20:32 
   Extra Example 2: Find the Missing Measure 22:11 
   Extra Example 3: Find the Distance Between the Two Points 25:36 
   Extra Example 4: Pythagorean Theorem 29:33 
  Midpoints and Segment Congruence 42:26
   Intro 0:00 
   Definition of Midpoint 0:07 
    Midpoint 0:10 
   Midpoint Formulas 1:30 
    Midpoint Formula: On a Number Line 1:45 
    Midpoint Formula: In a Coordinate Plane 2:50 
   Midpoint 4:40 
    Example: Midpoint on a Number Line 4:43 
   Midpoint 6:05 
    Example: Midpoint in a Coordinate Plane 6:06 
   Midpoint 8:28 
    Example 1 8:30 
    Example 2 13:01 
   Segment Bisector 15:14 
    Definition and Example of Segment Bisector 15:15 
   Proofs 17:27 
    Theorem 17:53 
    Proof 18:21 
   Midpoint Theorem 19:37 
    Example: Proof & Midpoint Theorem 19:38 
   Extra Example 1: Midpoint on a Number Line 23:44 
   Extra Example 2: Drawing Diagrams 26:25 
   Extra Example 3: Midpoint 29:14 
   Extra Example 4: Segment Bisector 33:21 
  Angles 42:34
   Intro 0:00 
   Angles 0:05 
    Angle 0:07 
    Ray 0:23 
    Opposite Rays 2:09 
   Angles 3:22 
    Example: Naming Angle 3:23 
   Angles 6:39 
    Interior, Exterior, Angle 6:40 
    Measure and Degrees 7:38 
   Protractor Postulate 8:37 
    Example: Protractor Postulate 8:38 
   Angle Addition Postulate 11:41 
    Example: Angle addition Postulate 11:42 
   Classifying Angles 14:10 
    Acute Angle 14:16 
    Right Angles 14:30 
    Obtuse Angle 14:41 
   Angle Bisector 15:02 
    Example: Angle Bisector 15:04 
   Angle Relationships 16:43 
    Adjacent Angles 16:47 
    Vertical Angles 17:49 
    Linear Pair 19:40 
   Angle Relationships 20:31 
    Right Angles 20:32 
    Supplementary Angles 21:15 
    Complementary Angles 21:33 
   Extra Example 1: Angles 24:08 
   Extra Example 2: Angles 29:06 
   Extra Example 3: Angles 32:05 
   Extra Example 4 Angles 35:44 

II. Reasoning & Proof

  Inductive Reasoning 19:00
   Intro 0:00 
   Inductive Reasoning 0:05 
    Conjecture 0:06 
    Inductive Reasoning 0:15 
   Examples 0:55 
    Example: Sequence 0:56 
    More Example: Sequence 2:00 
   Using Inductive Reasoning 2:50 
    Example: Conjecture 2:51 
    More Example: Conjecture 3:48 
   Counterexamples 4:56 
    Counterexample 4:58 
   Extra Example 1: Conjecture 6:59 
   Extra Example 2: Sequence and Pattern 10:20 
   Extra Example 3: Inductive Reasoning 12:46 
   Extra Example 4: Conjecture and Counterexample 15:17 
  Conditional Statements 42:47
   Intro 0:00 
   If Then Statements 0:05 
    If Then Statements 0:06 
   Other Forms 2:29 
    Example: Without Then 2:40 
    Example: Using When 3:03 
    Example: Hypothesis 3:24 
   Identify the Hypothesis and Conclusion 3:52 
    Example 1: Hypothesis and Conclusion 3:58 
    Example 2: Hypothesis and Conclusion 4:31 
    Example 3: Hypothesis and Conclusion 5:38 
   Write in If Then Form 6:16 
    Example 1: Write in If Then Form 6:23 
    Example 2: Write in If Then Form 6:57 
    Example 3: Write in If Then Form 7:39 
   Other Statements 8:40 
    Other Statements 8:41 
   Converse Statements 9:18 
    Converse Statements 9:20 
   Converses and Counterexamples 11:04 
    Converses and Counterexamples 11:05 
    Example 1: Converses and Counterexamples 12:02 
    Example 2: Converses and Counterexamples 15:10 
    Example 3: Converses and Counterexamples 17:08 
   Inverse Statement 19:58 
    Definition and Example 19:59 
   Inverse Statement 21:46 
    Example 1: Inverse and Counterexample 21:47 
    Example 2: Inverse and Counterexample 23:34 
   Contrapositive Statement 25:20 
    Definition and Example 25:21 
   Contrapositive Statement 26:58 
    Example: Contrapositive Statement 27:00 
   Summary 29:03 
    Summary of Lesson 29:04 
   Extra Example 1: Hypothesis and Conclusion 32:20 
   Extra Example 2: If-Then Form 33:23 
   Extra Example 3: Converse, Inverse, and Contrapositive 34:54 
   Extra Example 4: Converse, Inverse, and Contrapositive 37:56 
  Point, Line, and Plane Postulates 17:24
   Intro 0:00 
   What are Postulates? 0:09 
    Definition of Postulates 0:10 
   Postulates 1:22 
    Postulate 1: Two Points 1:23 
    Postulate 2: Three Points 2:02 
    Postulate 3: Line 2:45 
   Postulates, cont.. 3:08 
    Postulate 4: Plane 3:09 
    Postulate 5: Two Points in a Plane 3:53 
   Postulates, cont.. 4:46 
    Postulate 6: Two Lines Intersect 4:47 
    Postulate 7: Two Plane Intersect 5:28 
   Using the Postulates 6:34 
    Examples: True or False 6:35 
   Using the Postulates 10:18 
    Examples: True or False 10:19 
   Extra Example 1: Always, Sometimes, or Never 12:22 
   Extra Example 2: Always, Sometimes, or Never 13:15 
   Extra Example 3: Always, Sometimes, or Never 14:16 
   Extra Example 4: Always, Sometimes, or Never 15:03 
  Deductive Reasoning 36:03
   Intro 0:00 
   Deductive Reasoning 0:06 
    Definition of Deductive Reasoning 0:07 
   Inductive vs. Deductive 2:51 
    Inductive Reasoning 2:52 
    Deductive reasoning 3:19 
   Law of Detachment 3:47 
    Law of Detachment 3:48 
    Examples of Law of Detachment 4:31 
   Law of Syllogism 7:32 
    Law of Syllogism 7:33 
    Example 1: Making a Conclusion 9:02 
    Example 2: Making a Conclusion 12:54 
   Using Laws of Logic 14:12 
    Example 1: Determine the Logic 14:42 
    Example 2: Determine the Logic 17:02 
   Using Laws of Logic, cont. 18:47 
    Example 3: Determine the Logic 19:03 
    Example 4: Determine the Logic 20:56 
   Extra Example 1: Determine the Conclusion and Law 22:12 
   Extra Example 2: Determine the Conclusion and Law 25:39 
   Extra Example 3: Determine the Logic and Law 29:50 
   Extra Example 4: Determine the Logic and Law 31:27 
  Proofs in Algebra: Properties of Equality 44:31
   Intro 0:00 
   Properties of Equality 0:10 
    Addition Property of Equality 0:28 
    Subtraction Property of Equality 1:10 
    Multiplication Property of Equality 1:41 
    Division Property of Equality 1:55 
    Addition Property of Equality Using Angles 2:46 
   Properties of Equality, cont. 4:10 
    Reflexive Property of Equality 4:11 
    Symmetric Property of Equality 5:24 
    Transitive Property of Equality 6:10 
   Properties of Equality, cont. 7:04 
    Substitution Property of Equality 7:05 
    Distributive Property of Equality 8:34 
   Two Column Proof 9:40 
    Example: Two Column Proof 9:46 
   Proof Example 1 16:13 
   Proof Example 2 23:49 
   Proof Example 3 30:33 
   Extra Example 1: Name the Property of Equality 38:07 
   Extra Example 2: Name the Property of Equality 40:16 
   Extra Example 3: Name the Property of Equality 41:35 
   Extra Example 4: Name the Property of Equality 43:02 
  Proving Segment Relationship 41:02
   Intro 0:00 
   Good Proofs 0:12 
    Five Essential Parts 0:13 
   Proof Reasons 1:38 
    Undefined 1:40 
    Definitions 2:06 
    Postulates 2:42 
    Previously Proven Theorems 3:24 
   Congruence of Segments 4:10 
    Theorem: Congruence of Segments 4:12 
   Proof Example 10:16 
    Proof: Congruence of Segments 10:17 
   Setting Up Proofs 19:13 
    Example: Two Segments with Equal Measures 19:15 
   Setting Up Proofs 21:48 
    Example: Vertical Angles are Congruent 21:50 
   Setting Up Proofs 23:59 
    Example: Segment of a Triangle 24:00 
   Extra Example 1: Congruence of Segments 27:03 
   Extra Example 2: Setting Up Proofs 28:50 
   Extra Example 3: Setting Up Proofs 30:55 
   Extra Example 4: Two-Column Proof 33:11 
  Proving Angle Relationships 33:37
   Intro 0:00 
   Supplement Theorem 0:05 
    Supplementary Angles 0:06 
   Congruence of Angles 2:37 
    Proof: Congruence of Angles 2:38 
   Angle Theorems 6:54 
    Angle Theorem 1: Supplementary Angles 6:55 
    Angle Theorem 2: Complementary Angles 10:25 
   Angle Theorems 11:32 
    Angle Theorem 3: Right Angles 11:35 
    Angle Theorem 4: Vertical Angles 12:09 
    Angle Theorem 5: Perpendicular Lines 12:57 
   Using Angle Theorems 13:45 
    Example 1: Always, Sometimes, or Never 13:50 
    Example 2: Always, Sometimes, or Never 14:28 
    Example 3: Always, Sometimes, or Never 16:21 
   Extra Example 1: Always, Sometimes, or Never 16:53 
   Extra Example 2: Find the Measure of Each Angle 18:55 
   Extra Example 3: Find the Measure of Each Angle 25:03 
   Extra Example 4: Two-Column Proof 27:08 

III. Perpendicular & Parallel Lines

  Parallel Lines and Transversals 37:35
   Intro 0:00 
   Lines 0:06 
    Parallel Lines 0:09 
    Skew Lines 2:02 
    Transversal 3:42 
   Angles Formed by a Transversal 4:28 
    Interior Angles 5:53 
    Exterior Angles 6:09 
    Consecutive Interior Angles 7:04 
    Alternate Exterior Angles 9:47 
    Alternate Interior Angles 11:22 
    Corresponding Angles 12:27 
   Angles Formed by a Transversal 15:29 
    Relationship Between Angles 15:30 
   Extra Example 1: Intersecting, Parallel, or Skew 19:26 
   Extra Example 2: Draw a Diagram 21:37 
   Extra Example 3: Name the Figures 24:12 
   Extra Example 4: Angles Formed by a Transversal 28:38 
  Angles and Parallel Lines 41:53
   Intro 0:00 
   Corresponding Angles Postulate 0:05 
    Corresponding Angles Postulate 0:06 
   Alternate Interior Angles Theorem 3:05 
    Alternate Interior Angles Theorem 3:07 
   Consecutive Interior Angles Theorem 5:16 
    Consecutive Interior Angles Theorem 5:17 
   Alternate Exterior Angles Theorem 6:42 
    Alternate Exterior Angles Theorem 6:43 
   Parallel Lines Cut by a Transversal 7:18 
    Example: Parallel Lines Cut by a Transversal 7:19 
   Perpendicular Transversal Theorem 14:54 
    Perpendicular Transversal Theorem 14:55 
   Extra Example 1: State the Postulate or Theorem 16:37 
   Extra Example 2: Find the Measure of the Numbered Angle 18:53 
   Extra Example 3: Find the Measure of Each Angle 25:13 
   Extra Example 4: Find the Values of x, y, and z 36:26 
  Slope of Lines 44:06
   Intro 0:00 
   Definition of Slope 0:06 
    Slope Equation 0:13 
   Slope of a Line 3:45 
    Example: Find the Slope of a Line 3:47 
   Slope of a Line 8:38 
    More Example: Find the Slope of a Line 8:40 
   Slope Postulates 12:32 
    Proving Slope Postulates 12:33 
   Parallel or Perpendicular Lines 17:23 
    Example: Parallel or Perpendicular Lines 17:24 
   Using Slope Formula 20:02 
    Example: Using Slope Formula 20:03 
   Extra Example 1: Slope of a Line 25:10 
   Extra Example 2: Slope of a Line 26:31 
   Extra Example 3: Graph the Line 34:11 
   Extra Example 4: Using the Slope Formula 38:50 
  Proving Lines Parallel 25:55
   Intro 0:00 
   Postulates 0:06 
    Postulate 1: Parallel Lines 0:21 
    Postulate 2: Parallel Lines 2:16 
   Parallel Postulate 3:28 
    Definition and Example of Parallel Postulate 3:29 
   Theorems 4:29 
    Theorem 1: Parallel Lines 4:40 
    Theorem 2: Parallel Lines 5:37 
   Theorems, cont. 6:10 
    Theorem 3: Parallel Lines 6:11 
   Extra Example 1: Determine Parallel Lines 6:56 
   Extra Example 2: Find the Value of x 11:42 
   Extra Example 3: Opposite Sides are Parallel 14:48 
   Extra Example 4: Proving Parallel Lines 20:42 
  Parallels and Distance 19:48
   Intro 0:00 
   Distance Between a Points and Line 0:07 
    Definition and Example 0:08 
   Distance Between Parallel Lines 1:51 
    Definition and Example 1:52 
   Extra Example 1: Drawing a Segment to Represent Distance 3:02 
   Extra Example 2: Drawing a Segment to Represent Distance 4:27 
   Extra Example 3: Graph, Plot, and Construct a Perpendicular Segment 5:13 
   Extra Example 4: Distance Between Two Parallel Lines 15:37 

IV. Congruent Triangles

  Classifying Triangles 28:43
   Intro 0:00 
   Triangles 0:09 
    Triangle: A Three-Sided Polygon 0:10 
    Sides 1:00 
    Vertices 1:22 
    Angles 1:56 
   Classifying Triangles by Angles 2:59 
    Acute Triangle 3:19 
    Obtuse Triangle 4:08 
    Right Triangle 4:44 
   Equiangular Triangle 5:38 
    Definition and Example of an Equiangular Triangle 5:39 
   Classifying Triangles by Sides 6:57 
    Scalene Triangle 7:17 
    Isosceles Triangle 7:57 
    Equilateral Triangle 8:12 
   Isosceles Triangle 8:58 
    Labeling Isosceles Triangle 9:00 
    Labeling Right Triangle 10:44 
   Isosceles Triangle 11:10 
    Example: Find x, AB, BC, and AC 11:11 
   Extra Example 1: Classify Each Triangle 13:45 
   Extra Example 2: Always, Sometimes, or Never 16:28 
   Extra Example 3: Find All the Sides of the Isosceles Triangle 20:29 
   Extra Example 4: Distance Formula and Triangle 22:29 
  Measuring Angles in Triangles 44:43
   Intro 0:00 
   Angle Sum Theorem 0:09 
    Angle Sum Theorem for Triangle 0:11 
   Using Angle Sum Theorem 4:06 
    Find the Measure of the Missing Angle 4:07 
   Third Angle Theorem 4:58 
    Example: Third Angle Theorem 4:59 
   Exterior Angle Theorem 7:58 
    Example: Exterior Angle Theorem 8:00 
   Flow Proof of Exterior Angle Theorem 15:14 
    Flow Proof of Exterior Angle Theorem 15:17 
   Triangle Corollaries 27:21 
    Triangle Corollary 1 27:50 
    Triangle Corollary 2 30:42 
   Extra Example 1: Find the Value of x 32:55 
   Extra Example 2: Find the Value of x 34:20 
   Extra Example 3: Find the Measure of the Angle 35:38 
   Extra Example 4: Find the Measure of Each Numbered Angle 39:00 
  Exploring Congruent Triangles 26:46
   Intro 0:00 
   Congruent Triangles 0:15 
    Example of Congruent Triangles 0:17 
   Corresponding Parts 3:39 
    Corresponding Angles and Sides of Triangles 3:40 
   Definition of Congruent Triangles 11:24 
    Definition of Congruent Triangles 11:25 
   Triangle Congruence 16:37 
    Congruence of Triangles 16:38 
   Extra Example 1: Congruence Statement 18:24 
   Extra Example 2: Congruence Statement 21:26 
   Extra Example 3: Draw and Label the Figure 23:09 
   Extra Example 4: Drawing Triangles 24:04 
  Proving Triangles Congruent 47:51
   Intro 0:00 
   SSS Postulate 0:18 
    Side-Side-Side Postulate 0:27 
   SAS Postulate 2:26 
    Side-Angle-Side Postulate 2:29 
   SAS Postulate 3:57 
    Proof Example 3:58 
   ASA Postulate 11:47 
    Angle-Side-Angle Postulate 11:53 
   AAS Theorem 14:13 
    Angle-Angle-Side Theorem 14:14 
   Methods Overview 16:16 
    Methods Overview 16:17 
    SSS 16:33 
    SAS 17:06 
    ASA 17:50 
    AAS 18:17 
    CPCTC 19:14 
   Extra Example 1:Proving Triangles are Congruent 21:29 
   Extra Example 2: Proof 25:40 
   Extra Example 3: Proof 30:41 
   Extra Example 4: Proof 38:41 
  Isosceles and Equilateral Triangles 27:53
   Intro 0:00 
   Isosceles Triangle Theorem 0:07 
    Isosceles Triangle Theorem 0:09 
   Isosceles Triangle Theorem 2:26 
    Example: Using the Isosceles Triangle Theorem 2:27 
   Isosceles Triangle Theorem Converse 3:29 
    Isosceles Triangle Theorem Converse 3:30 
   Equilateral Triangle Theorem Corollaries 4:30 
    Equilateral Triangle Theorem Corollary 1 4:59 
    Equilateral Triangle Theorem Corollary 2 5:55 
   Extra Example 1: Find the Value of x 7:08 
   Extra Example 2: Find the Value of x 10:04 
   Extra Example 3: Proof 14:04 
   Extra Example 4: Proof 22:41 

V. Triangle Inequalities

  Special Segments in Triangles 43:44
   Intro 0:00 
   Perpendicular Bisector 0:06 
    Perpendicular Bisector 0:07 
   Perpendicular Bisector 4:07 
    Perpendicular Bisector Theorems 4:08 
   Median 6:30 
    Definition of Median 6:31 
   Median 9:41 
    Example: Median 9:42 
   Altitude 12:22 
    Definition of Altitude 12:23 
   Angle Bisector 14:33 
    Definition of Angle Bisector 14:34 
   Angle Bisector 16:41 
    Angle Bisector Theorems 16:42 
   Special Segments Overview 18:57 
    Perpendicular Bisector 19:04 
    Median 19:32 
    Altitude 19:49 
    Angle Bisector 20:02 
    Examples: Special Segments 20:18 
   Extra Example 1: Draw and Label 22:36 
   Extra Example 2: Draw the Altitudes for Each Triangle 24:37 
   Extra Example 3: Perpendicular Bisector 27:57 
   Extra Example 4: Draw, Label, and Write Proof 34:33 
  Right Triangles 26:34
   Intro 0:00 
   LL Theorem 0:21 
    Leg-Leg Theorem 0:25 
   HA Theorem 2:23 
    Hypotenuse-Angle Theorem 2:24 
   LA Theorem 4:49 
    Leg-Angle Theorem 4:50 
   LA Theorem 6:18 
    Example: Find x and y 6:19 
   HL Postulate 8:22 
    Hypotenuse-Leg Postulate 8:23 
   Extra Example 1: LA Theorem & HL Postulate 10:57 
   Extra Example 2: Find x So That Each Pair of Triangles is Congruent 14:15 
   Extra Example 3: Two-column Proof 17:02 
   Extra Example 4: Two-column Proof 21:01 
  Indirect Proofs and Inequalities 33:30
   Intro 0:00 
   Writing an Indirect Proof 0:09 
    Step 1 0:49 
    Step 2 2:32 
    Step 3 3:00 
   Indirect Proof 4:30 
    Example: 2 + 6 = 8 5:00 
    Example: The Suspect is Guilty 5:40 
    Example: Measure of Angle A < Measure of Angle B 6:06 
   Definition of Inequality 7:47 
    Definition of Inequality & Example 7:48 
   Properties of Inequality 9:55 
    Comparison Property 9:58 
    Transitive Property 10:33 
    Addition and Subtraction Properties 12:01 
    Multiplication and Division Properties 13:07 
   Exterior Angle Inequality Theorem 14:12 
    Example: Exterior Angle Inequality Theorem 14:13 
   Extra Example 1: Draw a Diagram for the Statement 18:32 
   Extra Example 2: Name the Property for Each Statement 19:56 
   Extra Example 3: State the Assumption 21:22 
   Extra Example 4: Write an Indirect Proof 25:39 
  Inequalities for Sides and Angles of a Triangle 17:26
   Intro 0:00 
   Side to Angles 0:10 
    If One Side of a Triangle is Longer Than Another Side 0:11 
   Converse: Angles to Sides 1:57 
    If One Angle of a Triangle Has a Greater Measure Than Another Angle 1:58 
   Extra Example 1: Name the Angles in the Triangle From Least to Greatest 2:38 
   Extra Example 2: Find the Longest and Shortest Segment in the Triangle 3:47 
   Extra Example 3: Angles and Sides of a Triangle 4:51 
   Extra Example 4: Two-column Proof 9:08 
  Triangle Inequality 28:11
   Intro 0:00 
   Triangle Inequality Theorem 0:05 
    Triangle Inequality Theorem 0:06 
   Triangle Inequality Theorem 4:22 
    Example 1: Triangle Inequality Theorem 4:23 
    Example 2: Triangle Inequality Theorem 9:40 
   Extra Example 1: Determine if the Three Numbers can Represent the Sides of a Triangle 12:00 
   Extra Example 2: Finding the Third Side of a Triangle 13:34 
   Extra Example 3: Always True, Sometimes True, or Never True 18:18 
   Extra Example 4: Triangle and Vertices 22:36 
  Inequalities Involving Two Triangles 29:36
   Intro 0:00 
   SAS Inequality Theorem 0:06 
    SAS Inequality Theorem & Example 0:25 
   SSS Inequality Theorem 4:33 
    SSS Inequality Theorem & Example 4:34 
   Extra Example 1: Write an Inequality Comparing the Segments 6:08 
   Extra Example 2: Determine if the Statement is True 9:52 
   Extra Example 3: Write an Inequality for x 14:20 
   Extra Example 4: Two-column Proof 17:44 

VI. Quadrilaterals

  Parallelograms 29:11
   Intro 0:00 
   Quadrilaterals 0:06 
    Four-sided Polygons 0:08 
    Non Examples of Quadrilaterals 0:47 
   Parallelograms 1:35 
    Parallelograms 1:36 
   Properties of Parallelograms 4:28 
    Opposite Sides of a Parallelogram are Congruent 4:29 
    Opposite Angles of a Parallelogram are Congruent 5:49 
   Angles and Diagonals 6:24 
    Consecutive Angles in a Parallelogram are Supplementary 6:25 
    The Diagonals of a Parallelogram Bisect Each Other 8:42 
   Extra Example 1: Complete Each Statement About the Parallelogram 10:26 
   Extra Example 2: Find the Values of x, y, and z of the Parallelogram 13:21 
   Extra Example 3: Find the Distance of Each Side to Verify the Parallelogram 16:35 
   Extra Example 4: Slope of Parallelogram 23:15 
  Proving Parallelograms 42:43
   Intro 0:00 
   Parallelogram Theorems 0:09 
    Theorem 1 0:20 
    Theorem 2 1:50 
   Parallelogram Theorems, Cont. 3:10 
    Theorem 3 3:11 
    Theorem 4 4:15 
   Proving Parallelogram 6:21 
    Example: Determine if Quadrilateral ABCD is a Parallelogram 6:22 
   Summary 14:01 
    Both Pairs of Opposite Sides are Parallel 14:14 
    Both Pairs of Opposite Sides are Congruent 15:09 
    Both Pairs of Opposite Angles are Congruent 15:24 
    Diagonals Bisect Each Other 15:44 
    A Pair of Opposite Sides is Both Parallel and Congruent 16:13 
   Extra Example 1: Determine if Each Quadrilateral is a Parallelogram 16:54 
   Extra Example 2: Find the Value of x and y 20:23 
   Extra Example 3: Determine if the Quadrilateral ABCD is a Parallelogram 24:05 
   Extra Example 4: Two-column Proof 30:28 
  Rectangles 29:47
   Intro 0:00 
   Rectangles 0:03 
    Definition of Rectangles 0:04 
   Diagonals of Rectangles 2:52 
    Rectangles: Diagonals Property 1 2:53 
    Rectangles: Diagonals Property 2 3:30 
   Proving a Rectangle 4:40 
    Example: Determine Whether Parallelogram ABCD is a Rectangle 4:41 
   Rectangles Summary 9:22 
    Opposite Sides are Congruent and Parallel 9:40 
    Opposite Angles are Congruent 9:51 
    Consecutive Angles are Supplementary 9:58 
    Diagonals are Congruent and Bisect Each Other 10:05 
    All Four Angles are Right Angles 10:40 
   Extra Example 1: Find the Value of x 11:03 
   Extra Example 2: Name All Congruent Sides and Angles 13:52 
   Extra Example 3: Always, Sometimes, or Never True 19:39 
   Extra Example 4: Determine if ABCD is a Rectangle 26:45 
  Squares and Rhombi 39:14
   Intro 0:00 
   Rhombus 0:09 
    Definition of a Rhombus 0:10 
   Diagonals of a Rhombus 2:03 
    Rhombus: Diagonals Property 1 2:21 
    Rhombus: Diagonals Property 2 3:49 
    Rhombus: Diagonals Property 3 4:36 
   Rhombus 6:17 
    Example: Use the Rhombus to Find the Missing Value 6:18 
   Square 8:17 
    Definition of a Square 8:20 
   Summary Chart 11:06 
    Parallelogram 11:07 
    Rectangle 12:56 
    Rhombus 13:54 
    Square 14:44 
   Extra Example 1: Diagonal Property 15:44 
   Extra Example 2: Use Rhombus ABCD to Find the Missing Value 19:39 
   Extra Example 3: Always, Sometimes, or Never True 23:06 
   Extra Example 4: Determine the Quadrilateral 28:02 
  Trapezoids and Kites 30:48
   Intro 0:00 
   Trapezoid 0:10 
    Definition of Trapezoid 0:12 
   Isosceles Trapezoid 2:57 
    Base Angles of an Isosceles Trapezoid 2:58 
    Diagonals of an Isosceles Trapezoid 4:05 
   Median of a Trapezoid 4:26 
    Median of a Trapezoid 4:27 
   Median of a Trapezoid 6:41 
    Median Formula 7:00 
   Kite 8:28 
    Definition of a Kite 8:29 
   Quadrilaterals Summary 11:19 
    A Quadrilateral with Two Pairs of Adjacent Congruent Sides 11:20 
   Extra Example 1: Isosceles Trapezoid 14:50 
   Extra Example 2: Median of Trapezoid 18:28 
   Extra Example 3: Always, Sometimes, or Never 24:13 
   Extra Example 4: Determine if the Figure is a Trapezoid 26:49 

VII. Proportions and Similarity

  Using Proportions and Ratios 20:10
   Intro 0:00 
   Ratio 0:05 
    Definition and Examples of Writing Ratio 0:06 
   Proportion 2:05 
    Definition of Proportion 2:06 
    Examples of Proportion 2:29 
   Using Ratio 5:53 
    Example: Ratio 5:54 
   Extra Example 1: Find Three Ratios Equivalent to 2/5 9:28 
   Extra Example 2: Proportion and Cross Products 10:32 
   Extra Example 3: Express Each Ratio as a Fraction 13:18 
   Extra Example 4: Fin the Measure of a 3:4:5 Triangle 17:26 
  Similar Polygons 27:53
   Intro 0:00 
   Similar Polygons 0:05 
    Definition of Similar Polygons 0:06 
    Example of Similar Polygons 2:32 
   Scale Factor 4:26 
    Scale Factor: Definition and Example 4:27 
   Extra Example 1: Determine if Each Pair of Figures is Similar 7:03 
   Extra Example 2: Find the Values of x and y 11:33 
   Extra Example 3: Similar Triangles 19:57 
   Extra Example 4: Draw Two Similar Figures 23:36 
  Similar Triangles 34:10
   Intro 0:00 
   AA Similarity 0:10 
    Definition of AA Similarity 0:20 
    Example of AA Similarity 2:32 
   SSS Similarity 4:46 
    Definition of SSS Similarity 4:47 
    Example of SSS Similarity 6:00 
   SAS Similarity 8:04 
    Definition of SAS Similarity 8:05 
    Example of SAS Similarity 9:12 
   Extra Example 1: Determine Whether Each Pair of Triangles is Similar 10:59 
   Extra Example 2: Determine Which Triangles are Similar 16:08 
   Extra Example 3: Determine if the Statement is True or False 23:11 
   Extra Example 4: Write Two-Column Proof 26:25 
  Parallel Lines and Proportional Parts 24:07
   Intro 0:00 
   Triangle Proportionality 0:07 
    Definition of Triangle Proportionality 0:08 
    Example of Triangle Proportionality 0:51 
   Triangle Proportionality Converse 2:19 
    Triangle Proportionality Converse 2:20 
   Triangle Mid-segment 3:42 
    Triangle Mid-segment: Definition and Example 3:43 
   Parallel Lines and Transversal 6:51 
    Parallel Lines and Transversal 6:52 
   Extra Example 1: Complete Each Statement 8:59 
   Extra Example 2: Determine if the Statement is True or False 12:28 
   Extra Example 3: Find the Value of x and y 15:35 
   Extra Example 4: Find Midpoints of a Triangle 20:43 
  Parts of Similar Triangles 27:06
   Intro 0:00 
   Proportional Perimeters 0:09 
    Proportional Perimeters: Definition and Example 0:10 
   Similar Altitudes 2:23 
    Similar Altitudes: Definition and Example 2:24 
   Similar Angle Bisectors 4:50 
    Similar Angle Bisectors: Definition and Example 4:51 
   Similar Medians 6:05 
    Similar Medians: Definition and Example 6:06 
   Angle Bisector Theorem 7:33 
    Angle Bisector Theorem 7:34 
   Extra Example 1: Parts of Similar Triangles 10:52 
   Extra Example 2: Parts of Similar Triangles 14:57 
   Extra Example 3: Parts of Similar Triangles 19:27 
   Extra Example 4: Find the Perimeter of Triangle ABC 23:14 

VIII. Applying Right Triangles & Trigonometry

  Pythagorean Theorem 21:14
   Intro 0:00 
   Pythagorean Theorem 0:05 
    Pythagorean Theorem & Example 0:06 
   Pythagorean Converse 1:20 
    Pythagorean Converse & Example 1:21 
   Pythagorean Triple 2:42 
    Pythagorean Triple 2:43 
   Extra Example 1: Find the Missing Side 4:59 
   Extra Example 2: Determine Right Triangle 7:40 
   Extra Example 3: Determine Pythagorean Triple 11:30 
   Extra Example 4: Vertices and Right Triangle 14:29 
  Geometric Mean 40:59
   Intro 0:00 
   Geometric Mean 0:04 
    Geometric Mean & Example 0:05 
   Similar Triangles 4:32 
    Similar Triangles 4:33 
   Geometric Mean-Altitude 11:10 
    Geometric Mean-Altitude & Example 11:11 
   Geometric Mean-Leg 14:47 
    Geometric Mean-Leg & Example 14:18 
   Extra Example 1: Geometric Mean Between Each Pair of Numbers 20:10 
   Extra Example 2: Similar Triangles 23:46 
   Extra Example 3: Geometric Mean of Triangles 28:30 
   Extra Example 4: Geometric Mean of Triangles 36:58 
  Special Right Triangles 37:57
   Intro 0:00 
   45-45-90 Triangles 0:06 
    Definition of 45-45-90 Triangles 0:25 
   45-45-90 Triangles 5:51 
    Example: Find n 5:52 
   30-60-90 Triangles 8:59 
    Definition of 30-60-90 Triangles 9:00 
   30-60-90 Triangles 12:25 
    Example: Find n 12:26 
   Extra Example 1: Special Right Triangles 15:08 
   Extra Example 2: Special Right Triangles 18:22 
   Extra Example 3: Word Problems & Special Triangles 27:40 
   Extra Example 4: Hexagon & Special Triangles 33:51 
  Ratios in Right Triangles 40:37
   Intro 0:00 
   Trigonometric Ratios 0:08 
    Definition of Trigonometry 0:13 
    Sine (sin), Cosine (cos), & Tangent (tan) 0:50 
   Trigonometric Ratios 3:04 
    Trig Functions 3:05 
    Inverse Trig Functions 5:02 
   SOHCAHTOA 8:16 
    sin x 9:07 
    cos x 10:00 
    tan x 10:32 
    Example: SOHCAHTOA & Triangle 12:10 
   Extra Example 1: Find the Value of Each Ratio or Angle Measure 14:36 
   Extra Example 2: Find Sin, Cos, and Tan 18:51 
   Extra Example 3: Find the Value of x Using SOHCAHTOA 22:55 
   Extra Example 4: Trigonometric Ratios in Right Triangles 32:13 
  Angles of Elevation and Depression 21:04
   Intro 0:00 
   Angle of Elevation 0:10 
    Definition of Angle of Elevation & Example 0:11 
   Angle of Depression 1:19 
    Definition of Angle of Depression & Example 1:20 
   Extra Example 1: Name the Angle of Elevation and Depression 2:22 
   Extra Example 2: Word Problem & Angle of Depression 4:41 
   Extra Example 3: Word Problem & Angle of Elevation 14:02 
   Extra Example 4: Find the Missing Measure 18:10 
  Law of Sines 35:25
   Intro 0:00 
   Law of Sines 0:20 
    Law of Sines 0:21 
   Law of Sines 3:34 
    Example: Find b 3:35 
   Solving the Triangle 9:19 
    Example: Using the Law of Sines to Solve Triangle 9:20 
   Extra Example 1: Law of Sines and Triangle 17:43 
   Extra Example 2: Law of Sines and Triangle 20:06 
   Extra Example 3: Law of Sines and Triangle 23:54 
   Extra Example 4: Law of Sines and Triangle 28:59 
  Law of Cosines 52:43
   Intro 0:00 
   Law of Cosines 0:35 
    Law of Cosines 0:36 
   Law of Cosines 6:22 
    Use the Law of Cosines When Both are True 6:23 
   Law of Cosines 8:35 
    Example: Law of Cosines 8:36 
   Extra Example 1: Law of Sines or Law of Cosines? 13:35 
   Extra Example 2: Use the Law of Cosines to Find the Missing Measure 17:02 
   Extra Example 3: Solve the Triangle 30:49 
   Extra Example 4: Find the Measure of Each Diagonal of the Parallelogram 41:39 

IX. Circles

  Segments in a Circle 22:43
   Intro 0:00 
   Segments in a Circle 0:10 
    Circle 0:11 
    Chord 0:59 
    Diameter 1:32 
    Radius 2:07 
    Secant 2:17 
    Tangent 3:10 
   Circumference 3:56 
    Introduction to Circumference 3:57 
    Example: Find the Circumference of the Circle 5:09 
   Circumference 6:40 
    Example: Find the Circumference of the Circle 6:41 
   Extra Example 1: Use the Circle to Answer the Following 9:10 
   Extra Example 2: Find the Missing Measure 12:53 
   Extra Example 3: Given the Circumference, Find the Perimeter of the Triangle 15:51 
   Extra Example 4: Find the Circumference of Each Circle 19:24 
  Angles and Arc 35:24
   Intro 0:00 
   Central Angle 0:06 
    Definition of Central Angle 0:07 
   Sum of Central Angles 1:17 
    Sum of Central Angles 1:18 
   Arcs 2:27 
    Minor Arc 2:30 
    Major Arc 3:47 
   Arc Measure 5:24 
    Measure of Minor Arc 5:24 
    Measure of Major Arc 6:53 
    Measure of a Semicircle 7:11 
   Arc Addition Postulate 8:25 
    Arc Addition Postulate 8:26 
   Arc Length 9:43 
    Arc Length and Example 9:44 
   Concentric Circles 16:05 
    Concentric Circles 16:06 
   Congruent Circles and Arcs 17:50 
    Congruent Circles 17:51 
    Congruent Arcs 18:47 
   Extra Example 1: Minor Arc, Major Arc, and Semicircle 20:14 
   Extra Example 2: Measure and Length of Arc 22:52 
   Extra Example 3: Congruent Arcs 25:48 
   Extra Example 4: Angles and Arcs 30:33 
  Arcs and Chords 21:51
   Intro 0:00 
   Arcs and Chords 0:07 
    Arc of the Chord 0:08 
    Theorem 1: Congruent Minor Arcs 1:01 
   Inscribed Polygon 2:10 
    Inscribed Polygon 2:11 
   Arcs and Chords 3:18 
    Theorem 2: When a Diameter is Perpendicular to a Chord 3:19 
   Arcs and Chords 5:05 
    Theorem 3: Congruent Chords 5:06 
   Extra Example 1: Congruent Arcs 10:35 
   Extra Example 2: Length of Arc 13:50 
   Extra Example 3: Arcs and Chords 17:09 
   Extra Example 4: Arcs and Chords 19:45 
  Inscribed Angles 27:53
   Intro 0:00 
   Inscribed Angles 0:07 
    Definition of Inscribed Angles 0:08 
   Inscribed Angles 0:58 
    Inscribed Angle Theorem 1 0:59 
   Inscribed Angles 3:29 
    Inscribed Angle Theorem 2 3:30 
   Inscribed Angles 4:38 
    Inscribed Angle Theorem 3 4:39 
   Inscribed Quadrilateral 5:50 
    Inscribed Quadrilateral 5:51 
   Extra Example 1: Central Angle, Inscribed Angle, and Intercepted Arc 7:02 
   Extra Example 2: Inscribed Angles 9:24 
   Extra Example 3: Inscribed Angles 14:00 
   Extra Example 4: Complete the Proof 17:58 
  Tangents 26:16
   Intro 0:00 
   Tangent Theorems 0:04 
    Tangent Theorem 1 0:05 
    Tangent Theorem 1 Converse 0:55 
   Common Tangents 1:34 
    Common External Tangent 2:12 
    Common Internal Tangent 2:30 
   Tangent Segments 3:08 
    Tangent Segments 3:09 
   Circumscribed Polygons 4:11 
    Circumscribed Polygons 4:12 
   Extra Example 1: Tangents & Circumscribed Polygons 5:50 
   Extra Example 2: Tangents & Circumscribed Polygons 8:35 
   Extra Example 3: Tangents & Circumscribed Polygons 11:50 
   Extra Example 4: Tangents & Circumscribed Polygons 15:43 
  Secants, Tangents, & Angle Measures 27:50
   Intro 0:00 
   Secant 0:08 
    Secant 0:09 
   Secant and Tangent 0:49 
    Secant and Tangent 0:50 
   Interior Angles 2:56 
    Secants & Interior Angles 2:57 
   Exterior Angles 7:21 
    Secants & Exterior Angles 7:22 
   Extra Example 1: Secants, Tangents, & Angle Measures 10:53 
   Extra Example 2: Secants, Tangents, & Angle Measures 13:31 
   Extra Example 3: Secants, Tangents, & Angle Measures 19:54 
   Extra Example 4: Secants, Tangents, & Angle Measures 22:29 
  Special Segments in a Circle 23:08
   Intro 0:00 
   Chord Segments 0:05 
    Chord Segments 0:06 
   Secant Segments 1:36 
    Secant Segments 1:37 
   Tangent and Secant Segments 4:10 
    Tangent and Secant Segments 4:11 
   Extra Example 1: Special Segments in a Circle 5:53 
   Extra Example 2: Special Segments in a Circle 7:58 
   Extra Example 3: Special Segments in a Circle 11:24 
   Extra Example 4: Special Segments in a Circle 18:09 
  Equations of Circles 27:01
   Intro 0:00 
   Equation of a Circle 0:06 
    Standard Equation of a Circle 0:07 
    Example 1: Equation of a Circle 0:57 
    Example 2: Equation of a Circle 1:36 
   Extra Example 1: Determine the Coordinates of the Center and the Radius 4:56 
   Extra Example 2: Write an Equation Based on the Given Information 7:53 
   Extra Example 3: Graph Each Circle 16:48 
   Extra Example 4: Write the Equation of Each Circle 19:17 

X. Polygons & Area

  Polygons 27:24
   Intro 0:00 
   Polygons 0:10 
    Polygon vs. Not Polygon 0:18 
   Convex and Concave 1:46 
    Convex vs. Concave Polygon 1:52 
   Regular Polygon 4:04 
    Regular Polygon 4:05 
   Interior Angle Sum Theorem 4:53 
    Triangle 5:03 
    Quadrilateral 6:05 
    Pentagon 6:38 
    Hexagon 7:59 
    20-Gon 9:36 
   Exterior Angle Sum Theorem 12:04 
    Exterior Angle Sum Theorem 12:05 
   Extra Example 1: Drawing Polygons 13:51 
   Extra Example 2: Convex Polygon 15:16 
   Extra Example 3: Exterior Angle Sum Theorem 18:21 
   Extra Example 4: Interior Angle Sum Theorem 22:20 
  Area of Parallelograms 17:46
   Intro 0:00 
   Parallelograms 0:06 
    Definition and Area Formula 0:07 
   Area of Figure 2:00 
    Area of Figure 2:01 
   Extra Example 1:Find the Area of the Shaded Area 3:14 
   Extra Example 2: Find the Height and Area of the Parallelogram 6:00 
   Extra Example 3: Find the Area of the Parallelogram Given Coordinates and Vertices 10:11 
   Extra Example 4: Find the Area of the Figure 14:31 
  Area of Triangles Rhombi, & Trapezoids 20:31
   Intro 0:00 
   Area of a Triangle 0:06 
    Area of a Triangle: Formula and Example 0:07 
   Area of a Trapezoid 2:31 
    Area of a Trapezoid: Formula 2:32 
    Area of a Trapezoid: Example 6:55 
   Area of a Rhombus 8:05 
    Area of a Rhombus: Formula and Example 8:06 
   Extra Example 1: Find the Area of the Polygon 9:51 
   Extra Example 2: Find the Area of the Figure 11:19 
   Extra Example 3: Find the Area of the Figure 14:16 
   Extra Example 4: Find the Height of the Trapezoid 18:10 
  Area of Regular Polygons & Circles 36:43
   Intro 0:00 
   Regular Polygon 0:08 
    SOHCAHTOA 0:54 
    30-60-90 Triangle 1:52 
    45-45-90 Triangle 2:40 
   Area of a Regular Polygon 3:39 
    Area of a Regular Polygon 3:40 
   Are of a Circle 7:55 
    Are of a Circle 7:56 
   Extra Example 1: Find the Area of the Regular Polygon 8:22 
   Extra Example 2: Find the Area of the Regular Polygon 16:48 
   Extra Example 3: Find the Area of the Shaded Region 24:11 
   Extra Example 4: Find the Area of the Shaded Region 32:24 
  Perimeter & Area of Similar Figures 18:17
   Intro 0:00 
   Perimeter of Similar Figures 0:08 
    Example: Scale Factor & Perimeter of Similar Figures 0:09 
   Area of Similar Figures 2:44 
    Example:Scale Factor & Area of Similar Figures 2:55 
   Extra Example 1: Complete the Table 6:09 
   Extra Example 2: Find the Ratios of the Perimeter and Area of the Similar Figures 8:56 
   Extra Example 3: Find the Unknown Area 12:04 
   Extra Example 4: Use the Given Area to Find AB 14:26 
  Geometric Probability 38:40
   Intro 0:00 
   Length Probability Postulate 0:05 
    Length Probability Postulate 0:06 
   Are Probability Postulate 2:34 
    Are Probability Postulate 2:35 
   Are of a Sector of a Circle 4:11 
    Are of a Sector of a Circle Formula 4:12 
    Are of a Sector of a Circle Example 7:51 
   Extra Example 1: Length Probability 11:07 
   Extra Example 2: Area Probability 12:14 
   Extra Example 3: Area Probability 17:17 
   Extra Example 4: Area of a Sector of a Circle 26:23 

XI. Solids

  Three-Dimensional Figures 23:39
   Intro 0:00 
   Polyhedrons 0:05 
    Polyhedrons: Definition and Examples 0:06 
    Faces 1:08 
    Edges 1:55 
    Vertices 2:23 
   Solids 2:51 
    Pyramid 2:54 
    Cylinder 3:45 
    Cone 4:09 
    Sphere 4:23 
   Prisms 5:00 
     Rectangular, Regular, and Cube Prisms 5:02 
   Platonic Solids 9:48 
    Five Types of Regular Polyhedra 9:49 
   Slices and Cross Sections 12:07 
    Slices 12:08 
    Cross Sections 12:47 
   Extra Example 1: Name the Edges, Faces, and Vertices of the Polyhedron 14:23 
   Extra Example 2: Determine if the Figure is a Polyhedron and Explain Why 17:37 
   Extra Example 3: Describe the Slice Resulting from the Cut 19:12 
   Extra Example 4: Describe the Shape of the Intersection 21:25 
  Surface Area of Prisms and Cylinders 38:50
   Intro 0:00 
   Prisms 0:06 
    Bases 0:07 
    Lateral Faces 0:52 
    Lateral Edges 1:19 
    Altitude 1:58 
   Prisms 2:24 
    Right Prism 2:25 
    Oblique Prism 2:56 
   Classifying Prisms 3:27 
    Right Rectangular Prism 3:28 
     4:55 
    Oblique Pentagonal Prism 6:26 
    Right Hexagonal Prism 7:14 
   Lateral Area of a Prism 7:42 
    Lateral Area of a Prism 7:43 
   Surface Area of a Prism 13:44 
    Surface Area of a Prism 13:45 
   Cylinder 16:18 
    Cylinder: Right and Oblique 16:19 
   Lateral Area of a Cylinder 18:02 
    Lateral Area of a Cylinder 18:03 
   Surface Area of a Cylinder 20:54 
    Surface Area of a Cylinder 20:55 
   Extra Example 1: Find the Lateral Area and Surface Are of the Prism 21:51 
   Extra Example 2: Find the Lateral Area of the Prism 28:15 
   Extra Example 3: Find the Surface Area of the Prism 31:57 
   Extra Example 4: Find the Lateral Area and Surface Area of the Cylinder 34:17 
  Surface Area of Pyramids and Cones 26:10
   Intro 0:00 
   Pyramids 0:07 
    Pyramids 0:08 
   Regular Pyramids 1:52 
    Regular Pyramids 1:53 
   Lateral Area of a Pyramid 4:33 
    Lateral Area of a Pyramid 4:34 
   Surface Area of a Pyramid 9:19 
    Surface Area of a Pyramid 9:20 
   Cone 10:09 
    Right and Oblique Cone 10:10 
   Lateral Area and Surface Area of a Right Cone 11:20 
    Lateral Area and Surface Are of a Right Cone 11:21 
   Extra Example 1: Pyramid and Prism 13:11 
   Extra Example 2: Find the Lateral Area of the Regular Pyramid 15:00 
   Extra Example 3: Find the Surface Area of the Pyramid 18:29 
   Extra Example 4: Find the Lateral Area and Surface Area of the Cone 22:08 
  Volume of Prisms and Cylinders 21:59
   Intro 0:00 
   Volume of Prism 0:08 
    Volume of Prism 0:10 
   Volume of Cylinder 3:38 
    Volume of Cylinder 3:39 
   Extra Example 1: Find the Volume of the Prism 5:10 
   Extra Example 2: Find the Volume of the Cylinder 8:03 
   Extra Example 3: Find the Volume of the Prism 9:35 
   Extra Example 4: Find the Volume of the Solid 19:06 
  Volume of Pyramids and Cones 22:02
   Intro 0:00 
   Volume of a Cone 0:08 
    Volume of a Cone: Example 0:10 
   Volume of a Pyramid 3:02 
    Volume of a Pyramid: Example 3:03 
   Extra Example 1: Find the Volume of the Pyramid 4:56 
   Extra Example 2: Find the Volume of the Solid 6:01 
   Extra Example 3: Find the Volume of the Pyramid 10:28 
   Extra Example 4: Find the Volume of the Octahedron 16:23 
  Surface Area and Volume of Spheres 14:46
   Intro 0:00 
   Special Segments 0:06 
    Radius 0:07 
    Chord 0:31 
    Diameter 0:55 
    Tangent 1:20 
   Sphere 1:43 
    Plane & Sphere 1:44 
    Hemisphere 2:56 
   Surface Area of a Sphere 3:25 
    Surface Area of a Sphere 3:26 
   Volume of a Sphere 4:08 
    Volume of a Sphere 4:09 
   Extra Example 1: Determine Whether Each Statement is True or False 4:24 
   Extra Example 2: Find the Surface Area of the Sphere 6:17 
   Extra Example 3: Find the Volume of the Sphere with a Diameter of 20 Meters 7:25 
   Extra Example 4: Find the Surface Area and Volume of the Solid 9:17 
  Congruent and Similar Solids 16:06
   Intro 0:00 
   Scale Factor 0:06 
    Scale Factor: Definition and Example 0:08 
   Congruent Solids 1:09 
    Congruent Solids 1:10 
   Similar Solids 2:17 
    Similar Solids 2:18 
   Extra Example 1: Determine if Each Pair of Solids is Similar, Congruent, or Neither 3:35 
   Extra Example 2: Determine if Each Statement is True or False 7:47 
   Extra Example 3: Find the Scale Factor and the Ratio of the Surface Areas and Volume 10:14 
   Extra Example 4: Find the Volume of the Larger Prism 12:14 

XII. Transformational Geometry

  Mapping 14:12
   Intro 0:00 
   Transformation 0:04 
    Rotation 0:32 
    Translation 1:03 
    Reflection 1:17 
    Dilation 1:24 
   Transformations 1:45 
    Examples 1:46 
   Congruence Transformation 2:51 
    Congruence Transformation 2:52 
   Extra Example 1: Describe the Transformation that Occurred in the Mappings 3:37 
   Extra Example 2: Determine if the Transformation is an Isometry 5:16 
   Extra Example 3: Isometry 8:16 
  Reflections 23:17
   Intro 0:00 
   Reflection 0:05 
    Definition of Reflection 0:06 
    Line of Reflection 0:35 
    Point of Reflection 1:22 
   Symmetry 1:59 
    Line of Symmetry 2:00 
    Point of Symmetry 2:48 
   Extra Example 1: Draw the Image over the Line of Reflection and the Point of Reflection 3:45 
   Extra Example 2: Determine Lines and Point of Symmetry 6:59 
   Extra Example 3: Graph the Reflection of the Polygon 11:15 
   Extra Example 4: Graph the Coordinates 16:07 
  Translations 18:43
   Intro 0:00 
   Translation 0:05 
    Translation: Preimage & Image 0:06 
    Example 0:56 
   Composite of Reflections 6:28 
    Composite of Reflections 6:29 
   Extra Example 1: Translation 7:48 
   Extra Example 2: Image, Preimage, and Translation 12:38 
   Extra Example 3: Find the Translation Image Using a Composite of Reflections 15:08 
   Extra Example 4: Find the Value of Each Variable in the Translation 17:18 
  Rotations 21:26
   Intro 0:00 
   Rotations 0:04 
    Rotations 0:05 
   Performing Rotations 2:13 
    Composite of Two Successive Reflections over Two Intersecting Lines 2:14 
    Angle of Rotation: Angle Formed by Intersecting Lines 4:29 
   Angle of Rotation 5:30 
    Rotation Postulate 5:31 
   Extra Example 1: Find the Rotated Image 7:32 
   Extra Example 2: Rotations and Coordinate Plane 10:33 
   Extra Example 3: Find the Value of Each Variable in the Rotation 14:29 
   Extra Example 4: Draw the Polygon Rotated 90 Degree Clockwise about P 16:13 
  Dilation 37:06
   Intro 0:00 
   Dilations 0:06 
    Dilations 0:07 
   Scale Factor 1:36 
    Scale Factor 1:37 
    Example 1 2:06 
    Example 2 6:22 
   Scale Factor 8:20 
    Positive Scale Factor 8:21 
    Negative Scale Factor 9:25 
    Enlargement 12:43 
    Reduction 13:52 
   Extra Example 1: Find the Scale Factor 16:39 
   Extra Example 2: Find the Measure of the Dilation Image 19:32 
   Extra Example 3: Find the Coordinates of the Image with Scale Factor and the Origin as the Center of Dilation 26:18 
   Extra Example 4: Graphing Polygon, Dilation, and Scale Factor 32:08 

Duration: 58 hours, 8 minutes

Number of Lessons: 89

Geometry is Professor Pyo’s favorite subject where she brings her love and experience to help high schoolers fully understand and ace their class.

Additional Features:

  • Free Sample Lessons
  • Closed Captioning (CC)
  • Practice Questions
  • Downloadable Lecture Slides
  • Study Guides

Topics Include:

  • Coordinate Plane
  • Inductive & Deductive Reasoning
  • Parallel Lines
  • Classifying Triangles
  • Indirect Proofs & Inequalities
  • Quadrilaterals
  • Similar Triangles
  • Pythagorean Theorem
  • Arcs & Chords
  • Geometric Probability
  • Surface Area of 3D Figures
  • Transformational Geometry

Professor Mary Pyo received her Master’s in Educational Curriculum and Instruction, her specialized credentials in Foundational mathematics, and has been teaching for 15+ years.

Student Testimonials:

"Everybody loves your teaching style, Mary, and I have to say that I do too!" — Edward H.

"I love the way that you teach us. I am a foreign exchange student, and my English is not very good, but I understand everything and now I like geometry." — Cinzia Z.

“Thank you Ms. Pyo for making this course effortless to learn. You are the best.” — Lin G.

“Very well done and explained.. I am teaching my son geometry and these lessons are so clear conceptually that even I can recall these concepts now :)” — Giri I.

“You are the best, you and Educator.com really saved me from a big nightmare.” — Dro M.