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+ Geometry Chapter 6: Congruent Triangles 6.1.1: Congruent Triangles + Learning Target: n I can identify congruent triangles by determining that the triangles are similar and have a similarity ratio of 1. + Mathematical Practice: n Construct viable arguments and critique the reasoning of others. n Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. + CCSSM: n Understand similarity in terms of similarity transformations. n Given two figures, use the definition of similarity in terms of similarity transformations to decide if the figures are similar. n Explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. + CCSSM: n Understand congruence in terms of rigid motions. n Given two figures, use the definition of congruence in terms of rigid motion to decide if the figures are congruent. n 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. + CCSSM: n Understand congruence in terms of rigid motions. n Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. n Use congruence and similarity criteria for triangles to solve problems and prove relationships between geometric figures. + Quote for today: n “Geometry enlightens the intellect and sets one’s mind right.” n Ibn Khaldun (1332 – 1406) + Similar Figures & Triangle Similarity Conditions: n Similar figures are shapes that have the same shape. Corresponding angles have the same measure. n Triangle n AA~ n SAS~ n SSS~ Similarity Conditions: + Rigid Transformations: n Reflections n Translations n Rotations + Congruent Shapes: n Two figures are congruent if and only if: n they have the same shape and the same size. n there is a sequence of rigid transformations that carry one figure onto the other. n they are similar and their similarity ratio is 1. + Assignments: n CW 6.1.1: Problems 6-1 through 6-3. n HW 6.1.1: Problems 6-4 through 6-10.