Proving Congruence – SSS, SAS Side-Side-Side Congruence Postulate (SSS) If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

Example 4-1b 3. SSS 1. Given 2. Reflexive Proof: ReasonsStatements  ABC  GBC Write a two-column proof to prove that  ABC  GBC if

Example 4-2c Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore,  ABC  DEF by SSS. Determine whether  ABC  DEF for A(5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1). Explain.

Proving Congruence – SSS, SAS Included angle – In a triangle, an angle that is formed by two sides is between them and, thus, referred to as included by those two sides. Side-Angle-Side Congruence Postulate (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Example 4-3c Write a flow proof. Given:. Prove:  ABC  ADC

Example 4-3d Proof:

Example 4-4c Answer: SAS Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. a.

Example 4-4d Answer: not possible b.