Similar figures – things that have the same shape but are generally a different size.

Similar polygons – polygons that have the same shape but are a different size

Scale - a ratio that compares each length in a scale drawing.

Scale factor - The ratio of corresponding linear measurements of two similar figures.

Scale drawing - A drawing where all lengths are proportional to their corresponding actual lengths.

7.2 Similar polygons

Today’s Vocabulary

similar figures

similar polygons

scale

scalefactor

scaledrawing

AC = AT = CTGO GD OD

16 = 12 = 84 3 2

4 = 4 = 4

The scale factor is 4

Every 1 mm on this drawing, corresponds to 10 mm on the real horse.

let’s brush up and practice

Write the ratio of the first measurement to the second measurement.

1. length of car: 14 ft 10 in. length of model car: 8 in

2. weight of car: 2900 lb weight of model car: 8 oz

3. There are 238 juniors at Torrington High School. The ratio of girls to boys in the junior class is 3:4. How many juniors are girls? How many are boys?

Convert to inches: (14)(12) + 10 = 178

178 : 8

convert : 8 oz = ½ lb = .5 lb

2900: .5

3x + 4x = 238 x = 34

There are 102 girls and 136 boys in the junior class.

3 = x5 25

x = 15

x = 94 2

x = 18

x - 2 = 3 8 4

x = 8

Similar polygons have corresponding angles that are congruent and corresponding sides that are proportional.

An extended proportion can be written for the ratios of corresponding sides of similar polygons.

AC = AT = CTGO GD OD

16 = 12 = 84 3 2

4 = 4 = 4

4 = 4 = 8

AC = AT = CTGO GD OD

16 = 12 = 84 3 1

1

YES NO

Let’s see if these quadrilaterals are similar. If they are, we’ll need to write a similarity statement and an extended proportion.

62

3

AB

XY

92

4.5

CD

ZW

82

4

BC

YZ

42

2

DA

WX

Compare angles: A X, B Y. C Z, D W

Compare ratios of sides:

Because corresponding sides are proportional and corresponding angles are congruent, ABCD ~ XYZW.

The extended proportion for the ratios of corresponding sides is:

AB BC CD DA

XY YZ ZW WX

Are these triangles similar?

Let’s check the congruency of angles and the proportionality of the sides.

If they are similar, give the scale factor.

Small sides AB = 20 = 10 XY 14 7

Medium sides BC = 30 = 10 YZ 21 7

Large sides AC = 40 = 10 XZ 28 7

If we look at the angles, we can see that corresponding angles are congruent.

m<A = m<X m<C = m<Zm<B = m<Y

Let’s look at the corresponding sides

Corresponding angles are congruent.

Corresponding sides have the same proportionality.

WE HAVE SIMILAR TRIANGLES!!!!!!!

The scale factor is 10:7

♥Give the scale factor of the polygons. ♥Find the value of x. ♥Round answers to the nearest tenth when necessary.

ABCD ~ NMPOWe are given that these quadrilaterals are similar.

•That means corresponding angles are congruent•AND•Corresponding sides are proportional.

Remember scale factor is the ratio of corresponding sides: 5 3

To find x, set up a proportion: 5 = 6 3 x

Solve =)

Your assignment

7-2 Practice and Reteach worksheets