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Transcript
Name: _____________________________ Geometry Chapter 4.3: Congruent Triangles We learned about congruent angles in chapter 4.2 and we will now work on applying congruence of angles and sides to proving that certain triangles are congruent to each other. Key Concept: Definition of Congruent Polygons Two polygons are congruent if and only if their corresponding parts are congruent Corresponding Angles: Corresponding Sides: Congruent Statement: Valid congruence statements for congruent polygons list corresponding vertices in the same order. Theorem 4.3: Third Angles Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. Theorem 4.4: Properties of Triangle Congruence Reflexive Property of Triangle Congruence Symmetric Property of Triangle Congruence Transitive Property of Triangle Congruence Examples: 1) Identify each congruent part then write a congruence statement for the triangles: Name: _____________________________ Geometry Chapter 4.3: Congruent Triangles 2) Polygon ABCD is congruent to polygon PQRS. Find x and y 3) Draw and label a figure with the following criteria. Then find the values of x and y. ABC DEF , AB 7 , BC 9 , AC 11 x , DE 2 y 5 4) Write a two column proof. Given: P R , PSQ RSQ , PQ RQ , PS RS Prove: PQS RQS Statements Reasons