Congruent Polygons 4.1.

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Presentation transcript:

Congruent Polygons 4.1

Objectives Define congruent polygons. Solve problems by using congruent polygons. homework

Glossary Terms corresponding angles corresponding sides congruent polygons homework

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

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

Angles and Line Segments X Y Z 50° A B C 50° Angles are congruent when they have equal measures (same number of degrees). 3 m 3 m Line segments are congruent when they have equal lengths. homework

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 correspondence with the first polygon. homework

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

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. Sides: Angles: Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE  RTPSQ. homework

Identify corresponding parts of congruent polygons. Given: ABCD  WXYZ. Identify all pairs of congruent sides and angles. Congruent angles: Congruent sides: A  W AB  WX B  X BC  XY C  Y CD  YZ D  Z DA  ZW homework

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

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

Using Corresponding Parts of Congruent Triangles Given: ∆ABC  ∆DBC. Find the value of x. 2x – 16 = 90 2x = 106 x = 53 homework

Using Corresponding Parts of Congruent Triangles Given: ∆ABC  ∆DEF Find the value of x. 2x – 2 = 6 2x = 8 x = 4 homework

Using Corresponding Parts of Congruent Triangles In the diagram, ΔITP  ΔNGO. Find the values of x and y. x – 2y = 7.5 x – 2(9) = 7.5 6y – 14 = 40 y = 9 6y = 54 x – 18 = 7.5 x = 25.5 Answer: x = 25.5, y = 9 homework

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

Assignment Geometry: 4.1A and 4.1B Section 10 - 30