Advanced Geometry Triangle Congruence Lesson 2 Proving Triangles

Advanced Geometry Triangle Congruence Lesson 2 Proving Triangles Congruent

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.

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

Side-Angle-Side Congruence Postulate p. 227 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.

Angle-Side-Angle Congruence Postulate p. 235 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 Congruence Theorem p. 236 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.

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

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 ASA Congruence Postulate not possible AAS Congruence Theorem

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.