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4.2 Apply Congruence and Triangles Goal Identify congruent figures. Congruent figures: In two congruent figures, all the parts (sides and angles) of one figure are _____________________ to the corresponding parts (sides and angles) of the other figure. Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. . something something Corresponding sides : Corresponding angles: AB _______ A ________ To help you identify corresponding parts, turn FGH CB ________ B ________ CA ________ C ________ So, ABC _________________ (YOU MUST GET THESE LETTERS IN THE RIGHT ORDER!) In the diagram, QRST WXYZ. A. Find the value of x. B. Find the value of y. Use the diagram shown in which FGHJ STUV. 1. Identify all pairs of congruent corresponding parts. Corresponding angles: F ______, G ______, H ______, J _______ Corresponding sides: HJ ______ JF _______ FG _______ GH _______ 2. Find the value of x and find mG. THEOREM: THIRD ANGLES THEOREM If two angles of one triangle are ________________to two angles of another triangle, then the third angles are also ________________________. Use the Third Angles Theorem Find mV. Example - In the diagram, EFG OPQ. Complete the statement. 1. EF ____ 2. P ____ F 4. F mO = ____ 3. G ____ 5. QO = ____ 6. GFE ____ Examples - Write a congruence statement for the figures . Make sure to match up your letters correctly! Transitive Property of Congruent Triangles (2 things =to the same thing must be =to each other) If ABC DEF, and DEF JKL, then ________________ Examples In the diagram below, E is the midpoint of Show that ABE CDE. AC and BD. In the diagram, what is the measure of D?