Isosceles and Equilateral Triangles

Isosceles Triangle Vocabulary:Vertex Angle – The angle formed by the

congruent sides of an isosceles triangle.

Base Angles – The two angles formed by the base and one of the congruent sides of an isosceles triangle.

Isosceles and Equilateral Triangles

Isosceles Triangle Theorem• If two sides of a triangle are congruent, then

the angles opposite those sides are congruent.Converse of the Isosceles Triangle Theorem• If two angles of an isosceles triangle are

congruent, then the sides opposite those angles are congruent.

Write a two-column proof.

Given: .

Prove:

Proof:

ReasonsStatements

1. Given

3. Isosceles Theorem

2. Def. of isosceles triangles

1.

2. ADB is isosceles.

3.

4.

5.

4. Given

5. Def. of midpoint

6. SAS

7. 7. CPCTC

6. ABC ADC

Answer: A

Multiple-Choice Test Item If and what is the measure of

A. 25 B. 35 C. 50 D. 130

a. Name two congruent angles.

Answer:

Answer:

b. Name two congruent segments.

Isosceles and Equilateral Triangles

Corollary 4.3

• A triangle is equilateral if and only if it is equiangular.

Corollary 4.4

• Each angle of an equilateral triangle measures 60 degrees.

a. Find x.

b.

Answer: 90

Answer: 30

ABC is an equilateral triangle. bisects