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Congruent Triangles Congruent Polygons 4.1 Holt Geometry Congruent Triangles Objectives • Define congruent polygons. • Solve problems by using congruent polygons. homework Holt Geometry Congruent Triangles Glossary Terms corresponding angles corresponding sides congruent polygons homework Holt Geometry Congruent Triangles Theorems, Postulates, & Definitions Polygon Congruence Postulate: Two polygons are congruent if and only if there is a correspondence between their sides and angles such that: 1. Each pair of corresponding angles is congruent. 2. Each pair of corresponding sides is congruent. homework Holt Geometry Congruent Triangles Geometric figures are congruent if they are the same size and shape. Two polygons are congruent polygons if and only if their corresponding sides and angles are congruent. Thus polygons that are the same size and shape are congruent. homework Holt Geometry Congruent Triangles Angles and Line Segments X A 50° B 50° C Y Z Angles are congruent when they have equal measures (same number of degrees). Line segments are congruent when they have equal lengths. homework Holt Geometry Congruent Triangles A correspondence is a way of matching up two sets of objects. To write a congruence statement, the vertices in the second polygon have to be written in order of homework correspondence with the first polygon. Holt Geometry Congruent Triangles How many ways can you name pentagon DCBAE? Pick a vertex and go clockwise Pick a vertex and go counterclockwise AEDCB ABCDE BAEDC BCDEA CBAED CDEAB DCBAE DEABC EDCBA EABCD homework Holt Geometry Congruent Triangles Identify corresponding parts of congruent polygons. Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. Angles: Sides: Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE RTPSQ. homework Holt Geometry Congruent Triangles Identify corresponding parts of congruent polygons. Given: ABCD WXYZ. Identify all pairs of congruent sides and angles. Congruent angles: A W B X C Y D Z Congruent sides: AB WX BC XY CD YZ DA ZW homework Holt Geometry Congruent Triangles Marking congruent sides and angles. In the diagram below, mark the congruent parts of the two figures. Then write a congruence statement. Congruent Angles A M B N C O D P Congruent Sides AB MN BC NO CD OP DA PM Since A corresponds to M, B corresponds to N, C corresponds to O,and D corresponds to P, a congruence statement is ABCD MNOP. homework Holt Geometry Congruent Triangles Write a congruence statement for each pair of polygons. The vertices in the first pentagon are written in order around the pentagon starting at any vertex. The congruence statement is pentagon DEFGH pentagon MNOPQ. homework Holt Geometry Congruent Triangles Using Corresponding Parts of Congruent Triangles Given: ∆ABC ∆DBC. Find the value of x. 2x – 16 = 90 2x = 106 x = 53 homework Holt Geometry Congruent Triangles Using Corresponding Parts of Congruent Triangles Given: ∆ABC ∆DEF Find the value of x. 2x – 2 = 6 2x = 8 x=4 Holt Geometry homework Congruent Triangles Using Corresponding Parts of Congruent Triangles In the diagram, ΔITP ΔNGO. Find the values of x and y. 6y – 14 = 40 x – 2y = 7.5 x – 2(9) = 7.5 6y = 54 x – 18 = 7.5 y=9 x = 25.5 Answer: x = 25.5, y = 9 homework Holt Geometry Congruent Triangles In the diagram, ΔFHJ ΔHFG. Find the values of x and y. A. x = 4.5, y = 2.75 B. x = 2.75, y = 4.5 C. x = 1.8, y = 19 D. x = 4.5, y = 5.5 homework Holt Geometry Congruent Triangles Assignment Geometry: 4.1A and 4.1B Section 10 - 30 Holt Geometry