Geometry Name: Period: Date:

1

Warm Up 12/05

Lesson 4-8: Isosceles and Equilateral Triangles

Objectives Students will…

- Be able to know and apply the properties and theorems about isosceles and equilateral triangles.

Isosceles Triangles We have learned that any triangle with two congruent sides is called an isosceles triangle. It turns out that isosceles triangles are quite special and to study them more closely, we need to define some of their components. Consider the isosceles 𝛥�ABC. Isosceles Triangle Theorem There is an important theorem concerning isosceles triangle. Isosceles Triangle Theorem- Two sides of a triangle are congruent, if and only if the angles opposite them (base angles) are congruent. Ex. → → →

As indicated, 𝐴𝐶̅̅ ̅̅ and 𝐴𝐵̅̅ ̅̅ are the two congruent sides.

These two sides are called the legs. The remaining side 𝐵𝐶̅̅ ̅̅ is the base. Furthermore, the two angles on the base, ∠𝑦, and ∠𝑧 are called the base angles, while the remaining angle, ∠𝑥 is called the vertex angle.

Geometry Name: Period: Date:

2

Equilateral and Equiangular Corollary Similar to the Triangle Sum Theorem, the Isosceles Triangle Theorem such an important concept that there is a natural result (corollary) that follows from it. Notice the “if and only if” again (Biconditional). Equilateral/Equiangular Corollary- A triangle is equilateral if and only if it is equiangular. Reason: (need to reason both ways!)

Homework 12/05 Isosceles and Equilateral Triangle Worksheet