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Transcript
Geometry 4-2 Big Idea: Use corresponding parts of congruent triangles to show triangle congruence. Congruent Figures: have the same shape, parts and measures. Corresponding parts : are parts of a figure that are related to the same parts of another figure A B D C Corresponding angles ÐA @ ÐD ÐB @ ÐE ÐC @ ÐF E F Corresponding sides AB @ DE AC @ DF BC @ EF Theorem 4.3 Third Angle Theorem If two angles of one triangle are congruent to the two angles of another triangle, then the third angles are also congruent. B A E C D F If ÐA @ ÐD and ÐB @ ÐE then ÐC @ ÐF Theorem 4.4 Properties of Congruent Angles Reflexive Property of Congruent Triangles: For any triangle ABC, DABC @ DABC Symmetric Property of Congruent Angles: For any triangle ABC, if DABC @ DDEF, then DDEF @ DABC Transitive Property of Congruent Triangles: If DABC @ DDEF and DDEF @ DJKL, then DABC @ DJKL Example: Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. J S R K L T In the diagram, DEFG @ SPQR. Find x and y. 8 ft D 102 G 84 12 ft E 68 Q F (2x - 4) ft (6y + x) P R S