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.

3. SSS

1. Given2. Reflexive

Proof: ReasonsStatements

1. 2.3. ABC GBC

Write a two-column proof to prove that ABC GBC if

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.

Write a flow proof.Given: .

Prove: ABC ADC

Proof:

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.

Answer: not possible

b.