(The Isosceles Triangle Theorems)

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Presentation transcript:

(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 Leg Base Angle Base Base Angle

Given: Prove: A 1 2 C B D

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

A B 1 D C D 2 A Statements Reasons Given

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

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

A B 1 D C D 2 A Statements Reasons

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

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

, If then Isosceles Triangle Theorem Converse 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.

M R T S P Q Statements Reasons

M R T S P Q Statements Reasons

Homework Chapter 4 Section 4 (The Isosceles Triangle Theorems) 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