How to identify and apply similar polygons. Chapter 7.2GeometryStandard/Goal: 2.1, 2.2, 4.1

1. Check and discuss the assignment from yesterday. 2. Work on Quiz Read, write, and discuss how to identify similar polygons. 4. Read, write, and discuss how to apply similar polygons. 5. Work on given assignment.

Similar (~) Two figures that have the same shape but not necessarily the same size. Note: For two polygons to be similar: 1. the corresponding angles are congruent. 2. the corresponding sides are proportional. The ratio of the lengths of corresponding sides is the similarity ratio.

ABC ~ XYZ Two polygons are similar if (1) corresponding angles are congruent and (2) corresponding sides are proportional. Lesson 7-2 Complete each statement. a. m  B = ? b. BC YZ = ? XZ a.  B  Y and m  Y = 78, so m  B = 78 because congruent angles have the same measure. b. Because AC corresponds to XZ,. = BC YZ AC XZ

Determine whether the parallelograms are similar. Explain. Corresponding sides of the two parallelograms are proportional. Although corresponding sides are proportional, the parallelograms are not similar because the corresponding angles are not congruent. Lesson 7-2 Check that corresponding angles are congruent.  B corresponds to  K, but m  B ≠ m  K, so corresponding angles are not congruent. Check that the corresponding sides are proportional. ==== AB JK 2424 BC KL 1212 CD LM 2424 DA MJ 1212

If ABC ~ YXZ, find the value of x. Because ABC ~ YXZ, you can write and solve a proportion. x =  Solve for x. x = 16 Lesson 7-2 =Corresponding sides are proportional. AC YZ BC XZ =Substitute. x

A painting is 24 in. wide by 36 in. long. The length of a postcard reduction of the painting is 6 in. How wide is the postcard? The postcard and the painting are similar rectangles, so you can write a proportion. Let x represent the width of the postcard. x = 4 The postcard is 4 in. wide. Lesson 7-2 Postcard widthpostcard length Painting widthpainting length = Corresponding sides are proportional. = Substitute. x x =  24 Solve for x.

The dimensions of a rectangular tabletop are in the Golden Ratio. The shorter side is 40 in. Find the longer side. Let represent the longer side of the tabletop. = Cross-Product Property The table is about 65 in. long. Lesson = Write a proportion using the Golden Ratio

Kennedy, D., Charles, R., Hall, B., Bass, L., Johnson, A. (2009) Geometry Prentice Hall Mathematics. Power Point made by: Robert Orloski Jerome High School.