Five-Minute Check (over Lesson 4–6)Main Idea and VocabularyKey Concept: Similar PolygonsExample 1:Identify Similar PolygonsExample 2:Find Missing MeasuresKey Concept: Ratios of Similar FiguresExample 3:Test Example

• polygon• similar• corresponding parts• congruent• scale factor

• Identify similar polygons and find missing measures of similar polygons.

BrainPop: Similar Triangles

Identify Similar Polygons

Determine whether triangle DEF is similar to triangle HJK. Explain your reasoning.

Identify Similar Polygons

Next, check to see if corresponding sides are proportional.

Answer:

1. A2. B

0%0%

A. yes

B. no

Determine whether triangle ACB is similar to triangle TRI.

Finding Missing Measures

Given that rectangle LMNO ~ rectangle GHIJ, find m.

Method 1 Write a proportion.

The missing measure m is the length of NO. Write a proportion involving NO that relates corresponding sides of the two rectangles.

Finding Missing Measures

rectangle GHIJrectangle LMNOrectangle LMNO

rectangle GHIJ

GJ = 2, LO = 3, IJ = 4, and NO = m

Find the cross products.

Multiply.

Divide each side by 2.

Finding Missing Measures

The scale factor is the constant of proportionality.

Method 2 Use the scale factor to write an equation.

Find the scale factor from rectangle GHIJ to rectangle LMNO by finding the ratio of corresponding sides with known lengths.

Finding Missing Measures

Words

Variable

Equation

Finding Missing Measures

Write the equation.

Simplify.

Answer: The measure is 6.

Multiply each side by

1. A2. B3. C4. D

0% 0%0%0%

A. 12

B. 15

C. 16

D. 18

Given that rectangle ABCD ~ rectangle WXYZ, find m.

A polygon has sides 2.5 times as long as a similar polygon. The smaller polygon has a perimeter of 42 inches. What is the perimeter of the larger polygon?

A 16.8 in. B 45 in. C 84 in. D 105 in.

Read the ItemSince each side of the larger polygon is 2.5 times as long as the corresponding sides of the smaller polygon, the scale factor from the smaller polygon to the largerpolygon is

Solve the ItemLet x represent the perimeter of the larger polygon. The ratio of the perimeters is equal to the ratio of the sides.

Answer: D

Find the cross products.

Simplify.

Scale factor relating sides

Multiply. Then divide each side by 2.

smaller perimeterlarger perimeter

1. A2. B3. C4. D0% 0%0%0%

A. 22 in.

B. 34 in.

C. 72 in.

D. 269.5 in.

A polygon has sides 3.5 times as long as a similar polygon. The larger polygon has a perimeter of 77 inches. What is the perimeter of the smaller polygon?

End of the Lesson

Five-Minute Check (over Lesson 4–6)

Image Bank

Math Tools

Solving Proportions

Dilations

Similar Triangles

1. A2. B3. C4. D0% 0%0%0%

(over Lesson 4-6)

A. 3 ways

B. 12 ways

C. 6 ways

D. 9 ways

Use the draw a diagram strategy.Daniel wants to display three different pictures in a row on his bedroom wall. How many different ways can he arrange the three pictures?

1. A2. B3. C4. D

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(over Lesson 4-6)

A. 18 students

B. 36 students

C. 54 students

D. 60 students

Use the draw a diagram strategy.The music teacher is arranging students on risers for the spring concert. If she places 6 people in the first row and each additional row has 3 more students in it, how many students will be in the fifth row?

1. A2. B3. C4. D

0% 0%0%0%

(over Lesson 4-6)

A. 13 minutes

B. 9 minutes 45 seconds

C. 6 minutes 30 seconds

D. 3 minutes 15 seconds

Jeanine is filling her wading pool with water. After

3 minutes and 15 seconds, the pool is only full.

If the pool can hold 350 gallons of water, how much

longer will it take to fill the pool?