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Section 4-1 Congruent Figures SPI 31A: identify corresponding parts of congruent geometric figures SPI 32C: determine congruence or relations between triangles or quadrilaterals given a diagram Objectives: • recognize congruent figures and their corresponding parts Congruent Polygons Congruent Polygons have congruent corresponding parts • Congruent sides • Congruent Angles • Matching vertices are corresponding vertices • always list corresponding parts in the same order Line AB line DE Line BC line EF Line CA line FD AD BE CF E B D A C F Real-World Connection using Congruent Figures The fins of the space shuttle suggest congruent pentagons. Find the mB. What is the angle corresponding to B? E Use the Polygon Angle Sum Thm: (n – 2)180 = (5 – 2)180 = 540 mS + mP + mA + mC + mE = 540 Angle Sum Thm 88 + 90 + 90 + 132 + mE = 540 Substitute 400 + mE = 540 Simplify mE = 140 SPE Since mB = mE, then angle B is 140 Are the Two Triangles Congruent? Two triangles are congruent if they have: • 3 pairs of corresponding sides • 3 pairs of corresponding angles Look at the diagram. What do you know by the markings? AC EC Given AB ED AB 3 ED BC DC A E B D BC 4 DC Given Right s are What is true about angles ACB and DCE? Explain. They are vertical angles, so they are congruent. Proving Triangle Congruency Use the information in the diagram to give a reason why each statement is true. Statement Reason Given PQ PS , QR SR Reflexive Prop of PR PR Q S , QPR SPR Given QRP SRP PQR PSR Theorem 4-1 Def of triangles