For this lesson, we are going to be taking a look at isosceles and equilateral triangles. An isosceles triangle is a triangle with two or more congruent sides. The isosceles triangle theorem says that if two sides of a triangle are congruent, then the angles opposite those sides are congruent. The isosceles triangle theorem is also called the base angles theorem, because it is saying that for an isosceles triangle, base angles are congruent. This lesson also covers the isosceles triangle theorem converse. Another thing you'll learn about in this lesson is that a triangle is equilateral if and only if it is equiangular, and you'll see what is the measure of each angle in such triangle.
AD||BC ; Given
∠AEB ≅ ∠CBE, ∠DEC ≅ ∠BCE; alternate interior angles ―BE ≅ ―CE ; Given
∠CBE ≅ ∠BCE ; Isosceles ∆ theorem
∠AEB ≅ ∠DEC ; Transitive prop of ≅ ∠s
E is the midpoint of AD ; Given ―AE ≅ ―DE ; Definition of midpoint ―BE ≅ ―CE ; Given
∆ ABE ≅ ∆ DCE ; SAS post
Given: ―AC ≅ ―AB , ―BC ≅ ―BD ,
Prove: BAC ≅ CBD
Statements ; Reasons
―AC ≅ ―AB ; Given
∠ABC ≅ ∠C ; Isosceles ∆ theorem thearom
∠ABC = m∠C ; definition of ≅ angles
∠BAC + m ∠ABC + m∠C = 180 ; triangle angles sum theorem
∠BAC + m∠C + m∠C = 180 ; transitive prop ( = )
∠BAC = 180 - 2 m∠C ; substraction prop ( = )
―BC ≅ ―BD ; Given
BDC ≅ C ; Isosceles ∆ theorem
∠BDC = m∠C ; definition of ≅ angles
∠CBD + m ∠BDC + m∠C = 180 ; triangle angles sum theorem
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Isosceles and Equilateral Triangles
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.