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Chapter 4.2 Notes: Apply Congruence and Triangles Goal: You will identify congruent figures. • Two geometric figures are congruent if they have exactly the same size and shape. Congruence Statements • In two congruent figures, all the parts of one figure are congruent to the corresponding parts of the other figure. • In congruent polygons, this means that the corresponding sides and the corresponding angles are congruent. • When you write a congruence statement for two polygons, always list the corresponding vertices in the same order. Congruence Statement: __________________ Corresponding angles: ___________________ Corresponding sides: ____________________ Ex.1: Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. Ex.2: In the diagram, DEFG SPQR . a. Find the value of x. b. Find the value of y. Ex.3: In the diagram below, ABGH CDEF . a. Identify all pairs of congruent corresponding parts. b. Find the value of x and find mH. Ex.4: Show that PTS RTQ. • Theorem 4.3 Third Angles Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Ex.5: Find mBDC . Ex.6: In the diagram, what is mDCN ? Ex.7: The two triangles are congruent. Identify all angles and sides that are congruent. Then write a congruence statement. Ex.8: In the diagram, ABCD FGHK. a. Find the value of x. b. Find the value of y. Properties of Congruent Triangles • Theorem 4.4 Properties of Congruent Triangles: – Reflexive Property of Congruent Triangles: For any triangle ABC, ABC ABC . – Symmetric Property of Congruent Triangles: If ABC DEF , then DEF ABC . – Transitive Property of Congruent Triangles: If ABC DEF & DEF JKL , then ABC JKL .