4-2: Triangle Congruence by SSS and SAS 4-3: Triangle Congruence by ASA and AAS 4-4: Using Corresponding Parts of Congruent Triangles

Side-Side-Side (SSS) If, in two triangles: three sides of one are congruent to three sides of the other, then the triangles are congruent. A B C D E F

Side-Angle-Side (SAS) If, in two triangles: two sides and the included angle of one are congruent to two sides and the included angle of the other, then the triangles are congruent A B C D E F

Angle-Side-Angle (ASA) If, in two triangles: two angles and the included side of one are congruent to two angles and the included side of the other, then the two triangles are congruent. A B C D E F

Angle-Angle-Side (AAS) If, in two triangles: two angles and a non-included side of one are congruent respectively to two angles and the corresponding non-included side of the other, then the triangles are congruent. A B C D E F

Using only the given information, which pairs of triangles are congruent? Justify your answer. 1. 2. No Yes; SAS 3. No

Writing Proofs 3 Prove ___ parts of one triangle are ____________ to the _________________ parts of another triangle. Use Triangle Congruence Theorems and other theorems in the proof. congruent corresponding 3

Ex. 1 F U N A C Given: Prove: Statement Reason 1). Given 1).

Ex. 2 L T P O Given: Prove: Statement Reason 1). 1). Given

A Ex. 3 Given: B D C Prove: E Statement Reason 1). 1). Given

Ex. 4 J K L M Given: Prove: Statement Reason 1). 1). Given

Corresponding Parts of Congruent Figures are Congruent (CPCFC) If two figures are congruent, then so are all of their corresponding parts.

Ex. 5 W A 1 2 Given: 4 3 Prove: T I Statement Reason 1). Given 1).