Proving Triangles Congruent Advanced Geometry Triangle Congruence Lesson 2

For two triangles to be congruent 6 pairs of parts must be congruent. The triangle congruence postulates and theorem allow us to prove two triangles are congruent using only 3 pairs of parts.

If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Side-Side-Side Congruence Postulate p. 226

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. Side-Angle-Side Congruence Postulate p. 227

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Angle-Side-Angle Congruence Postulate p. 235

If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. Angle-Angle-Side Congruence Theorem p. 236

These are the tests that work: SSS SAS ASA AAS These tests DO NOT work: AAA SSA

Examples : Determine which postulate or theorem can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. SAS Congruence Postulate not possible AAS Congruence Theorem ASA Congruence Postulate

Examples : Determine whether given the coordinates of the vertices. Explain.

Write a two-column proof. If and B is the midpoint of then

Write a two-column proof. If and then

Summary Prove 3 pairs of parts congruent. –Use any reason we have learned. Prove the triangles congruent. –Use a congruence test. If necessary, prove a pair of parts congruent. –Use CPCTC.