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Congruent Figures Lesson 4-1 Geometry Additional Examples ABC QTJ. List the congruent corresponding parts. List the corresponding vertices in the same order. Angles: A @ Q B @ T C @ J List the corresponding sides in the same order. Sides: AB @ QT BC @ TJ AC @ QJ Congruent Figures Lesson 4-1 Geometry Additional Examples XYZ KLM, mY = 67, and mM = 48. Find mX. Use the Triangle Angle-Sum Theorem and the definition of congruent polygons to find mX. mX + mY + mZ = 180 Triangle Angle-Sum Theorem mZ = mM Corresponding angles of congruent triangles that are congruent mZ = 48 Substitute 48 for mM. mX + 67 + 48 = 180 mX + 115 = 180 mX = 65 Substitute. Simplify. Subtract 115 from each side. Congruent Figures Lesson 4-1 Geometry Additional Examples Can you conclude that ABC CDE in the figure below? List corresponding vertices in the same order. If ABC CDE, then BAC DCE. The diagram above shows BAC DEC, not DCE. Corresponding angles are not necessarily congruent, therefore you cannot conclude that ABC CDE. Congruent Figures Lesson 4-1 Additional Examples Geometry Show how you can conclude that CNG DNG. List statements and reasons. Congruent triangles have three congruent corresponding sides and three congruent corresponding angles. Examine the diagram, and list the congruent corresponding parts for CNG and DNG. a. CG DG b. CN DN c. GN GN d. C D e. CNG DNG f. CGN DGN g. CNG DNG Given Given Reflexive Property of Congruence Given Right angles are congruent. If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. (Theorem 4-1.) Definition of triangles