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Objectives: recognize congruent figures and their corresponding parts

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:

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Objectives: recognize congruent figures and their corresponding parts

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  1. Section 4-1 Congruent Figures SPI 31A: identify corresponding parts of congruent geometric figuresSPI 32C: determine congruence or relations between triangles or quadrilaterals given a diagram • Objectives: • recognize congruent figures and their corresponding parts Congruent figures: Have the same size and shape Shapes may have a different orientation

  2. 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 A  D B  E C  F E B D A C F

  3. Real-World Connection using Congruent Figures The fins of the space shuttle suggest congruent pentagons. Find the mB. What is the angle corresponding to B? E Use the Polygon Angle Sum Thm: (n – 2)180 = (5 – 2)180 = 540 mS + mP + mA + mC + mE = 540 Angle Sum Thm 88 + 90 + 90 + 132 + mE = 540 Substitute 400 + mE = 540 Simplify mE = 140 SPE Since mB = mE, then angle B is 140

  4. 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? What is true about angles ACB and DCE? Explain. They are vertical angles, so they are congruent.

  5. Proving Triangle Congruency Use the information in the diagram to give a reason why each statement is true. Given Reflexive Prop of  Given Theorem 4-1 Def of  triangles

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