Lesson 6.1 Use Similar Polygons Use Similar Polygons

Two figures that have the same shape but not necessarily the same size are similar (~).Two polygons are similar if (1) corresponding angles are congruent and (2) corresponding sides are proportional. The ratio of the lengths of corresponding sides is the similarity ratio.

What is a similarity statement? A statement that two polygons are similar. (It is similar (tee hee) to a congruency statement) Example:

Scale Factor You might hear this referred to as the similarity ratio. This is the ratio of the lengths of the corresponding sides of two similar polygons. The scale factor depends on the order of comparison.

Are the polygons similar? If they are, write a similarity statement, and give the similarity ratio. If they are not, explain. Triangle ABC is similar to triangle XYZ and the similarity ratio Is 2/1 or Triangle xyz is similar to abc and the similarity ratio 1/2

Are the polygons similar? If they are, write a similarity statement, and give the similarity ratio. If they are not, explain. These are not similar because the angles are not congruent

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Algebra The polygons are similar. Find the value of the variable. If you think x=3.96 feet, you are correct

Algebra You can use similarity to find perimeter as well. These two rectangles are similar as they appear. Find the perimeter of each PQRS perimeter: 26 inches, LMNO perimeter:15.6 inches

Perimeter of Similar Polygons

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In any golden rectangle, the length and width are in the golden ratio which is about : 1 The golden rectangle is considered pleasing to the human eye. It has appeared in architecture and art since ancient times. It has intrigued artists including Leonardo da Vinci (1452–1519). Da Vinci illustrated The Divine Proportion, a book about the golden rectangle.

A golden rectangle is a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle. A pattern of repeated golden rectangles is shown to the right. Each golden rectangle that is formed is copied and divided again. Each golden rectangle is similar to the original rectangle. This Gold rectangle is not a golden rectangle

Application of GR The length and width of a rectangular tabletop are in the golden ratio. The shorter side is 40 in. Find the length of the longer side inches