7.2 Similar polygons Today’s Vocabulary 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.

similar figures similar polygons

scale drawing scale factor scale AC = AT = CT GO GD OD 16 = 12 = 8 16 = 12 = 8 4 3 2 4 = 4 = 4 Every 1 mm on this drawing, corresponds to 10 mm on the real horse. The scale factor is 4

let’s brush up and practice Write the ratio of the first measurement to the second measurement. Convert to inches: (14)(12) + 10 = 178 length of car: 14 ft 10 in. length of model car: 8 in 178 : 8 2900: .5 weight of car: 2900 lb weight of model car: 8 oz convert : 8 oz = ½ lb = .5 lb 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? 3x + 4x = 238 x = 34 There are 102 girls and 136 boys in the junior class.

3 = x 5 25 x = 15 x = 9 4 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 = CT GO GD OD 16 = 12 = 8 4 3 2 4 = 4 = 4 4 = 4 = 8 AC = AT = CT GO GD OD 16 = 12 = 8 4 3 1 1 YES NO

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

The scale factor is 10:7 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. If we look at the angles, we can see that corresponding angles are congruent. Corresponding angles are congruent. m<A = m<X m<B = m<Y m<C = m<Z Corresponding sides have the same proportionality. Let’s look at the corresponding sides WE HAVE SIMILAR TRIANGLES!!!!!!! Small sides AB = 20 = 10 XY 14 7 Medium sides BC = 30 = 10 YZ 21 7 The scale factor is 10:7 Large sides AC = 40 = 10 XZ 28 7

ABCD ~ NMPO We are given that these quadrilaterals are similar. That means corresponding angles are congruent AND Corresponding sides are proportional. ABCD ~ NMPO Give the scale factor of the polygons. Find the value of x. Round answers to the nearest tenth when necessary. Remember scale factor is the ratio of corresponding sides: 5 3 To find x, set up a proportion: 5 = 6 3 x Solve =)

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