Triangle Congruence Proofs 4

Objectives: G.CO.8: Explain how the criteria for triangle congruence (ASA,SAS, SSS, and AAS) follow from the definition of congruence in terms of rigid motions. G.CO.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.SRT.5: Use congruence and similarity criteria for triangles to solve problems and prove relationships in geometric figures.

For the Board: You will be able to use congruent triangles to prove segments and angles congruent.

Bell Work: State whether or not you can use the following information to prove two triangles are congruent 1. ASA 2. SSA 3. SAS 4. SSS 5. AAS 6. AAA

Anticipatory Set: Definition of Congruent Triangles (CPCTC) Two triangles are congruent if and only if all three angle and all three sides of one triangle are congruent to the corresponding three angles and three sides of another triangle.

Instruction: B Given: AB||CD, BC||DA C Prove: AB  CD

A D

Proof: Statements Reasons 1. AB||CD, BC||DA 1. Given 2.

M Given: A midpoint of MT and SR R Prove:

If two sides of a triangle are congruent then the angles opposite them are congruent. Given: AB  AC Prove:

Proof: Statements Reasons B C 1. Let X be the midpoint of BC 1. Every segment has a unique midpoint. 2. Draw AX 2. Through two points there is exactly one segment. 3. AB  AC 3. Given 4. BX  CX 4. Definition of Midpoint 4. AD  AD 5. Reflexive Property of Congruence 6. ΔABD  ΔACD 6. SSS 6.

Base Angles Converse Theorem If two angles of a triangle are congruent then the sides opposite them are congruent.

Given: point. 3.

Assessment: Question student pairs.

Independent Practice: Handout 4