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10147308917305Name Class Date 9-5Reteaching108585021590Congruence TransformationsBecause rigid motions preserve distance and angle measure, the image of a rigidmotion or composition of rigid motions is congruent to the preimage. Congruencecan be defined by rigid motions as follows.Two figures are congruent if and only if there is a sequence of one or more rigidmotions that map one figure onto the other.Because rigid motions map figures to congruent figures, rigid motions andcompositions of rigid motions are also called congruence transformations. If twofigures are congruent, you can find a congruence transformation that maps onefigure to the other.390525042545ProblemIn the figure at the right, ?PQR ?STU. What is a congruencetransformation that maps ?PQR to ?STU??STU appears to have the same shape and orientation as ?PQR,but rotated 90°, so start by applying the rotation r(90°, O) on thevertices of ?PQR.r(90°, O)(P) = (4, 1), r(90°, O)(Q) = (1, 4), r(90°, O)(r) = (2, 1)Graph the image r(90°, O)(?PQR). A translation of 1 unit tothe right and 5 units down maps the image to ?STU.Therefore, (T<1, 5> ° r(90°, O))( ?PQR) = ?STU.ExercisesFind a congruence transformation that maps ?ABC to ?DEF.2. 1. 228600290830Prentice Hall Geometry ? Teaching Resources4910147308917305Name Class Date 9-5Reteaching108585021590Congruence TransformationsIf you can show that a congruence transformation exists from one figure toanother, then you have shown that the figures are congruent.Problem38100190503248025-2540Verify the SSS Postulate by using a congruencetransformation.Prove: ?JKL ?RST3657600130175Start by translating ?JKL so that points J and R coincide.4295775134620Because you are given that , there is a rigid motion that mapsonto by rotating ?JKL about point R so that and coincide.Thus, there is a congruence transformation that maps ?JKL to ?RST,so ?JKL ?RST.Exercises3771900889003.Verify the SAS Postulate for triangle congruence by usingcongruence transformations.Prove: ?RST ?XYZ4.Verify the ASA Postulate for triangle congruence by usingcongruence transformations.Given: Prove: ?ABC ?JKLPrentice Hall Geometry ? Teaching Resources50 ................
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