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1. There are 480 sophomores and 520 juniors in a high school. Find the ratio of juniors to sophomores.

2. A strip of wood molding that is 33 inches long is cut into two pieces whose lengths are in the ratio of 7:4. What are their lengths?

Solve each proportion.

3.

4.

5.

6. The ratio of the measures of the three angles of a triangle is 13:6:17. Find the measure of the largest angle.

Standardized Test Practice:

6 72--- = ---x 84

39 4x--- = ----57 19

2x – 1 x + 4-------- = --------- 4 8

13:12

21 and 12 inches

x = 7

x = 13/4 = 3.25

x = 2

85

Lesson 6-2

Similar Polygons

Objectives

• Identify similar figures

• Solve problems involving scale factors

Vocabulary

• Scale factor – the ratio of corresponding sides of similar polygons

Similar Polygons

A

B

C

D

P

Q

R

S

Congruent Corresponding Angles

mA = mPmB = mQmC = mRmD = mS

Corresponding Side Scale Equal

AC AB CD DB ---- = ---- = ---- = ----PR PQ RS SQ

Determine whether the pair of figures is similar. Justify your answer.

Q

The vertex angles are marked as 40º and 50º, so they are not congruent. Since both triangles are isosceles, the base angles in each triangle are congruent. In the first triangle, the base angles measure ½ (180 – 40) or 70° and in the second triangle, the base angles measure ½ (180 – 50) or 65°

Answer: None of the corresponding angles are congruent,

so the triangles are not similar.

Example 1a

Determine whether the pair of figures is similar.Justify your answer.

T

Since the measures of all the corresponding angles are equal, then the angles must be congruent.

Example 1b

Answer: The ratio of the measures of the corresponding sides are equal and the corresponding angles are congruent, so ∆ABC ~ ∆RST

Answer: Only one pair of angles are congruent, so the triangles are not similar.

Determine whether the pair of figures is similar.Justify your answer.

Example 1c

An architect prepared a 12-inch model of a skyscraper to look like a real 1100-foot building. What is the scale factor of the model compared to the real building?

Before finding the scale factor you must make sure that both measurements use the same unit of measure.

1100(12) 13,200 inches

Answer: The ratio comparing the two heights is

The scale factor is

, which means that the

model is the height of the real

skyscraper.

Example 2a

A space shuttle is about 122 feet in length. The Science Club plans to make a model of the space shuttle with a length of 24 inches. What is the scale factor of the model compared to the real space shuttle?

Answer:

Example 2b

The two polygons are similar. Write a similarity statement. Then find x, y, and UV.

Use the congruent angles to write the corresponding vertices in order.

Example 3a

To find x:

Similarity proportion

Multiply.

Divide each side by 4.

To find y:

Similarity proportion

Cross products

Multiply.

Subtract 6 from each side.

Divide each side by 6 and simplify.

Answer:

Example 3a cont

The two polygons are similar. Find the scale factor of polygon ABCDE to polygon RSTUV.

The scale factor is the ratio of the lengths of any two corresponding sides.

Answer:

Example 3b

a. Write a similarity statement. Then find a, b, and ZO.

b. Find the scale factor of polygon TRAP to polygon ZOLD .Answer:

The two polygons are similar.

Answer: ;

Example 3c

Summary & Homework

• Summary:– In similar polygons, corresponding angles are

congruent, and corresponding sides are in (the same ratio) proportion

– The ratio of two corresponding sides in two similar polygons is the scale factor

• Homework: – pg 293-5: 4, 6, 7, 12, 13, 27-31, 36, 38