Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Module 4 Quiz Answer Key.

## Texas Go Math Grade 7 Module 4 Quiz Answer Key

**Texas Go Math Grade 7 Module 4 Ready to Go On? Answer Key**

**4.1 Similar Shapes and Proportions**

Question 1.

Explain whether the shapes are similar.

Answer:

Yes, both the given shape (triangle) are similar.

Because all the angLes of both triangles are equal and also the ratio of corresponding sides of the triangle are equal.

\(\frac{9}{6}\) = \(\frac{15}{10}\) = \(\frac{12}{8}\) = \(\frac{3}{2}\)

Hence, both shapes are similar.

**4.2 Using Similar Shapes**

**Find the missing measure in each pair of similar shapes.**

Question 2.

Answer:

These two shapes are similar, so the corresponding sides are proportional.

The missing measure is 20.

Question 3.

Answer:

\centering To find the missing measure, use a proportion.

\(\frac{30}{9}\) = \(\frac{x}{12}\)

\(\frac{30}{9} \cdot \frac{1.33}{=1.33} \frac{x}{12}\)

\(\frac{39.9}{12}\) = \(\frac{x}{12}\)

39.9 = x

The missing measure is x = 39.9.

**4.3 Similar Shapes and Scale Drawings**

Question 4.

What is the area of the room represented in the scale drawing?

Answer:

3cm : 6ft4 ⇔ 1 cm : 2 ft

l = 10cm

w = 6 cm

Convert length and width from cm to ft

l = 10 ∙ 2 = 20 ft

w = 6 ∙ 2 = 12 ft

Use the formula for the area of the rectangle.

A = 1 w Substitute 20 for 1 and 12 for w.

A = 20 ∙ 12

A = 240

The area of the room is 240 ft^{2}.

**4.4 Ratios and Pi**

Question 5.

Find the missing measure.

Answer:

C = 37.68 The circumference of big circle

d = 12 Diameter of big circle

C_{1} = ? The circumference of similar circle

d_{1} = 6 Diameter of similar circle

\centering To find the missing measure, use a proportion.

The circumference of similar circle is 18.84.

**Essential Question**

Question 6.

How can you use similarity and proportionality to find missing measures?

Answer:

For every similar shapes, the corresponding measures are proportional so from proportion we can find the missing measures.

**Texas Go Math Grade 7 Module 4 Mixed Review Texas Test Prep Answer Key**

**Selected Response**

Question 1.

Which shows a pair of shapes that are not similar? All corresponding angles have equal measure.

Answer:

Example under (C) shows a pair of shapes that are not similar.

Explanation:

For value of side from the picture, when we write a proportion using corresponding sides, we get;

(A) \(\frac{8}{6}=\frac{8}{6}=\frac{8}{6}\)

which is correct

(B) \(\frac{20}{12}=\frac{20}{12}\)

which is correct

(C) \(\frac{4}{6}=\frac{6}{10}\)

0.66 = 0.6

which isn’t correct

(D) \(\frac{9}{12}=\frac{9}{12}=\frac{6}{8}\)

0.75 = 0.75 = 0.75

which is correct

Question 2.

A scale drawing of a rectangular deck is shown below.

What is the perimeter of the actual deck?

(A) 187.5 ft

(B) 375 ft

(C) 550 ft

(D) 750 ft

Answer:

(B) 375 ft

Explanation:

2 in : 25 ft ⇔ 1 in : 12.5 ft

Convert Length and width from in. to ft.

l = 11 ∙ 12.5 = 137.5 ft

w = 4 ∙ 12.5 = 50 ft

Use the formula for the perimeter of rectangle.

P = 2(l + w) Substitute 137.5 for l and 50 for w.

P = 2(137.5 + 50)

P = 375

The perimeter of the actuaL deck is 375 ft

Question 3.

The two triangles below are similar. Find the area of the larger triangle.

(A) 8 square units

(B) 36 square units

(C) 64 square units

(D) 128 square units

Answer:

The area of the larger triangle is (C) 64 square units.

Explanation:

x_{1} = 6

y_{1} = 12

x = ?

y = 16

\centering To find the missing measure, use a proportion.

The area of the larger triangle is:

\(\frac{7,98 \cdot 16}{8}\) = 63.84 ≈ 64

Question 4.

Find the circumference of the smaller circle.

(A) 15.7

(B) 22.5

(C) 23.55

(D) 31.4

Answer:

(C) 23.55

Explanation:

C_{1} = the circumference of the larger circle

C_{2} = the circumference of the smaller circle

d_{1} = the diameter of the larger circle

d_{2} = the diameter of the smaller circle

Two circles are similar, so the corresponding measures are proportional.

Write the proportion

The circumference of the smaller circle is 23.55.

**Gridded Response**

Question 5.

An advertising company is creating a large wall banner and a smaller flyer that are similar figures. What percent of the area of the banner is the area of the flyer?

Answer:

x_{1} = 15

y_{1} = 40

x = ?

y = 24

\centering To find the missing measure, use a proportion.

Use formula for the area of rectangLe P = x ∙ y where x represents Length of rectangle and y represents width of rectangle.

The area of a large wall banner is:

P_{1} = 15 ∙ 40 = 600

The area of smaller flyer is:

P = 9 ∙ 24 = 216

When we divide the area of smaller flyer by the area of a large wall banner, we get which percent of the area of the banner is the area of a smaller flyer.

\(\frac{216}{600}\) = 0.36 = 36%