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58:08

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• Level Intermediate
• 89 Lessons (58hr : 08min)
• Audio: English
• English

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.

## Section 1: Tools of Geometry

Coordinate Plane 16:41
Intro 0:00
The Coordinate System 0:12
Coordinate Plane: X-axis and Y-axis 0:15
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 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
Example and Definition of Segment Addition Postulate 5:03
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
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
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

## Section 2: 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
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

## Section 3: 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

## Section 4: 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

## Section 5: 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
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

Parallelograms 29:11
Intro 0:00
Four-sided Polygons 0:08
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
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

## Section 7: 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

## Section 8: 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

## Section 9: 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
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 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
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

## Section 10: 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
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

## Section 11: 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
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

## Section 12: 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, 08 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.

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

Topics Include:

• Coordinate Plane
• Inductive & Deductive Reasoning
• Parallel Lines
• Classifying Triangles
• Indirect Proofs & Inequalities
• 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.

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