Class Opener: If you have a vision problem, a magnification system can help you read. You choose a...

Class Opener:

• If you have a vision problem, a magnification system can help you read. You choose a level of magnification. Then you place an image under the viewer. A similar, magnified image appears on the video screen.

• The video screen is 16in by 12in tall. What is the largest complete video image possible for a block of tect that is 6in by 4in?

7-2 Similar Polygons

Similarity

• Similar figures have the same shape but not necessarily the same size.– The ~ symbol means

“is similar to” • Two polygons are similar

polygons if corresponding angles are congruent and if the lengths of corresponding sides are proportional.

• When three or more ratios are equal, you can write an extended proportion.

Understanding Similarity

MNP ~ SRT• What are the pairs of congruent angles?

• What is the extended proportion for the ratios of corresponding sides?

DEFG ~ HJKL

• What are the pairs of congruent angles?

• What is the extended proportion for the ratios of the lengths of corresponding sides?

Scale Factor

• A scale factor is the ratio of corresponding linear measurements of two similar figures.– The ratio of corresponding sides is ,

so the scale factor of ABC to XYZ is or 5 : 2.

20 5

8 2

BC

YZ

5

2

Determining Similarity

• Are the polygons similar? If they are, write a similarity statement and give the scale factor.

Are the polygons similar? If they are, write a similarity statement and give the scale factor.

Using Similar Polygons

• ABCD ~ EFGD. What is the value of x?

What is the value of y?

Using Similarity

• In the diagram, Find SR.

.PS PT

PR PQ

In the diagram, Find CE..DF CE

DH CG

Scales

• In a scale drawing, all lengths are proportional to their corresponding actual lengths.

• The scale is the ratio that compares each length in the scale drawing to the actual length.– The lengths used in a scale can be in different

units (ex. 1 cm = 50 km).• You can use proportions to find the actual

dimensions represented in a scale drawing.

Using a Scale Drawing• The diagram shows a scale drawing of the Golden Gate

Bridge. If the length between the two towers in the diagram is 6.4 cm, what is the length of the actual bridge?

If the tower measures 0.8 cm in the diagram, what is the actual height of the tower?

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.

• Golden Ratio is 1.618 : 1