Geometry Honors: Unit 4 Day 2 Exploring Congruent Triangles Congruent triangles – triangles that have the same size and same shape

Each triangle has 6 parts: 3 sides and 3 angles. If the corresponding parts of one triangle are congruent to the six parts of another triangle, then the triangles are congruent. Since triangle ABC is congruent to triangle DEF, the vertices of the two triangles correspond in the same order as the letters naming the triangles.

A↔ B↔ C↔

This correspondence of vertices can be used to name the corresponding congruent sides and angles.

Congruent Angles Congruent Sides

∠A ≅ ______∠B ≅ ______∠C ≅ ______

AB ≅ ______

BC ≅ ______

AC ≅ ______

Definition of Congruent Triangles (CPCTC)

Two triangles are congruent if and only if their corresponding parts are congruent.

*Congruence of triangles is reflexive, symmetric, and transitive.

Examples

1. Δ______ ≅ Δ______

2. ΔRPG is congruent to ΔFAS . Which segment is congruent to AF ?

3. ΔJKL ≅ ΔDEF, m∠J = 36, m∠E = 64, and m∠F = 3x + 52 a. Draw and label a figure to show the congruent triangles.

b. Find x.

4. Given ΔABC ≅ ΔDEF, AB =15, BC = 20, AC = 25, and FE=3x-7 , find x.

5. Write a two-column proof. Given: ∠! ≅ ∠!, !" ≅ !", !" ≅ !",!" ≅ !" Prove: △ !"# ≅△ !"#

Statements Reasons