Rochester City School District
Name ______________________________Module 1 Lesson 22Congruence Criteria for Triangles – SAS Learning Target: I can prove two triangles are congruent using Side-Angle-Side.Opening ExerciseWhich transformation would map ?ABC onto ?EFC? Identify which pairs of corresponding sides and which pairs of corresponding angles are congruent.Side-Angle-Side triangle congruence criteria (SAS): Given two triangles △ABC and △A'B'C' so that AB=A'B' (Side), m∠A=m∠A' (Angle), AC=A'C' (Side). Then the triangles are congruent.The steps below show the most general case for determining a congruence between two triangles that satisfy the SAS criteria. Note that not all steps are needed for every pair of triangles. For example, sometimes the triangles will already share a vertex. Sometimes a reflection will be needed, sometimes not. What is important is that we can always use the steps below—some or all of them—to determine a congruence between the two triangles that satisfies the SAS criteria.Proof: Provided the two distinct triangles below, assume AB=A'B' (Side), m∠A=m∠A' (Angle), AC=A'C' (Side).Step 1: Use a translation T to map a common vertex. Step 2: Use a clockwise rotation R∠CAC'' to bring the sides AC” to AC (or counterclockwise rotation to bring AB” to AB).Step 3: If B''' and B are on opposite sides of the line that joins AC, a reflection rAC brings B''' to the same side as B.325175258284700Write the transformations used to correctly notate the congruence (the composition of transformations) that takes △A'B'C'? △ABC:F __________________________G __________________________H ______________________________(____(____(△A'B'C') = △ABC Example 1What if we had the SAS criteria for two triangles that were not distinct? Consider the following two cases. How would the transformations needed to demonstrate congruence change?CaseDiagramTransformations NeededShared Side30141416319500Shared Vertex3149604804800Exercises1. Given: Triangles with a pair of corresponding sides of equal length and a pair of included angles of equal measure. Name the sequence of rigid motions that prove the two triangles to be congruent.23050502222500Directions: Justify whether the triangles meet the SAS congruence criteria; explicitly state which pairs of sides or angles are congruent and why. If the triangles do meet the SAS congruence criteria, describe the rigid motion(s) that would map one triangle onto the other.357632084455002. Given: m∠LMN=m∠LNO, MN=ON.Do △LNM and △LOM meet the SAS criteria?3771054-252095003. Given: m∠HGI=m∠JIG, HG=JI.Do △HGI and △JIG meet the SAS criteria?Name ______________________________Module 1 Lesson 22Congruence Criteria for Triangles – SASProblem SetDirections: Justify whether the triangles meet the SAS congruence criteria; explicitly state which pairs of sides or angles are congruent and why. If the triangles do meet the SAS congruence criteria, describe the rigid motion(s) that would map one triangle onto the other.1. Given: AB∥CD, AB=CD. Do △ABD and △CDB meet the SAS criteria?684145516200 2. Given: m∠R=25°, RT=7", SU=5", ST=5". Do △RSU and △RST meet the SAS criteria?-2341773048000 3. Given: KM and JN bisect each other. Do △JKL and △NML meet the SAS criteria?203835889000-9000187132004. Given: m∠1=m∠2, BC=DC. Do △ABC and △ADC meet the SAS criteria?5. Given: AE bisects angle ∠BCD, BC=DC. Do △CAB and △CAD meet the SAS criteria?-16446533020006. Given: SU and RT bisect each other. Do △SVR and △UVT meet the SAS criteria?42164015875000Name ______________________________Module 1 Lesson 22Congruence Criteria for Triangles – SASExit TicketDirections: Justify whether the triangles meet the SAS congruence criteria. If the triangles do meet the SAS congruence criteria, describe the rigid motion(s) that would map one triangle onto the other.1. 2. 3. 4. 5. Given: JM=KL, JM⊥ML, KL⊥ML. Do △JML and △KLM meet the SAS criteria?1682754572000 ................
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