Five-Minute Check (over Lesson 7–1)

CCSS

Then/Now

New Vocabulary

Key Concept: Similar Polygons

Example 1: Use a Similarity Statement

Example 2: Real-World Example: Identify Similar Polygons

Example 3: Use Similar Figures to Find Missing Measures

Theorem 7.1: Perimeter of Similar Polygons

Example 4: Use a Scale Factor to Find Perimeter

Over Lesson 7–1

A. 10:8

B. 13:12

C. 19:17

D. 22:20

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

Over Lesson 7–1

A. 7 in., 4 in.

B. 14 in., 8 in.

C. 18 in., 15 in.

D. 21 in., 12 in.

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 the lengths of the two pieces?

Over Lesson 7–1

A. 7

B. 8

C. 9

D. 10

Over Lesson 7–1

A. 2.75

B. 3.25

C. 3.75

D. 4.25

Over Lesson 7–1

A. 4

B. 3

C. 2

D. 1

Over Lesson 7–1

A. 9.3 inches

B. 17 inches

C. 20 inches

D. 56 inches

The standard ratio of a photo’s width to its length

is

. What is the length of a photo that has a width of

14 inches?

Content Standards

G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Mathematical Practices

7 Look for and make use of structure.

3 Construct viable arguments and critique the reasoning of others.

You used proportions to solve problems.

• Use proportions to identify similar polygons.

• Solve problems using the properties of similar polygons.

• similar polygons

• scale factor

Use a Similarity Statement

If ΔABC ~ ΔRST, list all pairs of congruent angles and write a proportion that relates the corresponding sides.

Use a Similarity Statement

Use the similarity statement.

ΔABC ~ ΔRST

Congruent Angles: A R, B S, C T

Answer:

If ΔGHK ~ ΔPQR, determine which of the following similarity statements is not true.

A. HGK QPR

B.

C. K R

D. GHK QPR

Identify Similar Polygons

A. MENUS Tan is designing a new menu for the restaurant where he works. Determine whether the size for the new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning.Original Menu: New Menu:

Identify Similar Polygons

Step 1 Compare corresponding angles.

Since all angles of a rectangle are right angles and right angles are congruent, corresponding angles are congruent.

Step 2 Compare corresponding sides.

Answer: Since corresponding sides are not proportional, ABCD is not similar to FGHK. So, the menus are not similar.

Identify Similar Polygons

B. MENUS Tan is designing a new menu for the restaurant where he works. Determine whether the size for the new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning.Original Menu: New Menu:

Identify Similar Polygons

Step 1 Compare corresponding angles.

Since all angles of a rectangle are right angles and right angles are congruent, corresponding angles are congruent.

Step 2 Compare corresponding sides.

Identify Similar Polygons

Answer: Since corresponding sides are proportional,

ABCD ~ RSTU. So, the menus are similar

with a scale factor of . __45

A. Thalia is a wedding planner who is making invitations. Determine whether the size for the new invitations is similar to the original invitations used. If so, choose the correct similarity statement and scale factor.

A. BCDE ~ FGHI, scale factor =

B. BCDE ~ FGHI, scale factor =

C. BCDE ~ FGHI, scale factor =

D. BCDE is not similar to FGHI.

__12

__45

__38

Original: New:

B. Thalia is a wedding planner who is making invitations. Determine whether the size for the new invitations is similar to the original invitations used. If so, choose the correct similarity statement and scale factor.

A. BCDE ~ WXYZ, scale factor =

B. BCDE ~ WXYZ, scale factor =

C. BCDE ~ WXYZ, scale factor =

D. BCDE is not similar to WXYZ.

__12

__45

__38

Original: New:

Use Similar Figures to Find Missing Measures

A. The two polygons are similar. Find x.

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

polygon ABCDE ~ polygon RSTUV

Use Similar Figures to Find Missing Measures

Write a proportion to find x.

Similarity proportion

Cross Products Property

Multiply.

Divide each side by 4. Simplify.

Answer: x = __92

Use Similar Figures to Find Missing Measures

B. The two polygons are similar. Find y.

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

polygon ABCDE ~ polygon RSTUV

Use Similar Figures to Find Missing Measures

Similarity proportion

Cross Products Property

Multiply.

Subtract 6 from each side.

Divide each side by 6 and simplify.

AB = 6, RS = 4, DE = 8, UV = y + 1

Answer: y = __313

A. a = 1.4

B. a = 3.75

C. a = 2.4

D. a = 2

A. The two polygons are similar. Solve for a.

A. 1.2

B. 2.1

C. 7.2

D. 9.3

B. The two polygons are similar. Solve for b.

Use a Scale Factor to Find Perimeter

If ABCDE ~ RSTUV, find the scale factor of ABCDE to RSTUV and the perimeter of each polygon.

Use a Scale Factor to Find Perimeter

The scale factor ABCDE to RSTUV is or . ___AEVU

__47

Write a proportion to find the length of DC.

Since DC AB and AE DE, the perimeter of ABCDE is 6 + 6 + 6 + 4 + 4 or 26.

Write a proportion.

4(10.5)= 7 ● DC Cross Products Property

6 = DC Divide each side by 7.

Use a Scale Factor to Find Perimeter

Use the perimeter of ABCDE and scale factor to write a proportion. Let x represent the perimeter of RSTUV.

Theorem 7.1

Substitution

4x = (26)(7) Cross Products Property

x = 45.5 Solve.

Use a Scale Factor to Find Perimeter

Answer: The perimeter of ABCDE is 26 and the perimeter of RSTUV is 45.5.

A. LMNOP = 40, VWXYZ = 30

B. LMNOP = 32, VWXYZ = 24

C. LMNOP = 45, VWXYZ = 40

D. LMNOP = 60, VWXYZ = 45

If LMNOP ~ VWXYZ, find the perimeter of each polygon.