Chapter 4 Section 4 The Isosceles Triangle Theorems

Chapter 4 Section 4 (The Isosceles Triangle Theorems) Isosceles Triangle • A triangle with at least two congruent sides.

Vertex Angle Leg Base Angle

Given: Prove: A 1 2 B D C

A 1 B Statements 2 D C Reasons

A A 1 B 2 D Statements D Reasons Given C

A A 1 B 2 D Statements D C Reasons Def. angle bisector

A A 1 B 2 D Statements D C Reasons Reflexive Property

A A 1 B 2 D Statements D Reasons C

A A A 1 B 2 D B Statements C D Reasons Corresponding parts of congruent triangles are congruent. C

Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. B If , then A C

Isosceles Triangle Theorem Converse • If two angles of a triangle are congruent… then the sides opposite those angles are congruent. If , then

Corollary • An equilateral triangle is also equiangular. (An equiangular triangle is also equilateral. )

Corollary • The bisector of the vertex angle of an isosceles triangle… is perpendicular to its base… at its midpoint.

Solve for x.

Solve for x.

S P R Statements Q M Reasons T

S P R Statements Q M Reasons T

Chapter 4 Section 4 (The Isosceles Triangle Theorems) Homework Section 4. 4 Classroom Exercises (p. 136) #1 -7 Section 4. 4 Written Exercises (p. 137) #1 -9 Chapter 4 Mid-Review Worksheet