# Texas Go Math Grade 8 Module 13 Answer Key Dilations, Similarity, and Proportionality

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## Texas Go Math Grade 8 Module 13 Answer Key Dilations, Similarity, and Proportionality

Write each ratio in the simplest form.

Question 1.
$$\frac{6}{15}$$ ____________
To write a ratio in simplest form, find the greatest factor of the numerator and denominator.
$$\frac{6}{15}=\frac{6 \div 3}{15 \div 3}$$ (Divide the numerator and denominator by the GCF)
= $$\frac{2}{5}$$

$$\frac{8}{20}$$ ____________
To write a ratio in simplest form, find the greatest factor of the numerator and denominator.
$$\frac{8}{20}=\frac{8 \div 4}{20 \div 4}$$ (Divide the numerator and denominator by the GCF)
= $$\frac{2}{5}$$

Question 3.
$$\frac{30}{18}$$ ____________
To write a ratio in simplest form, find the greatest factor of the numerator and denominator.
$$\frac{30}{18}=\frac{30 \div 6}{18 \div 6}$$ (Divide the numerator and denominator by the GCF)
= $$\frac{5}{3}$$

Question 4.
$$\frac{36}{30}$$ ____________
To write a ratio in simplest form, find the greatest factor of the numerator and denominator.
$$\frac{36}{30}=\frac{36 \div 6}{30 \div 6}$$ (Divide the numerator and denominator by the GCF)
= $$\frac{6}{5}$$

Find the perimeter.

Question 5.
square with sides of 8.9 cm
side = 8.9 cm
We know that,
Perimeter of the square = 4s
P = 4 Ã— 8.9
P = 35.6 cm
Thus the perimeter of the square = 35.6 cm

rectangle with length 5$$\frac{1}{2}$$ ft and width 2$$\frac{3}{4}$$ ft
Given,
length 5$$\frac{1}{2}$$ ft and width 2$$\frac{3}{4}$$ ft
We know that,
Perimeter of the rectangle = 2L + 2W
P = 2 (5$$\frac{1}{2}$$ + 2$$\frac{3}{4}$$)
P = 2 ($$\frac{11}{2}$$ + $$\frac{11}{4}$$)
P = 2 ($$\frac{33}{4}$$
P = 33/2
P = 16 $$\frac{1}{2}$$
Thus the perimeter of the rectangle is 16 $$\frac{1}{2}$$ ft

Question 7.
equilateral triangle with sides of 8$$\frac{3}{8}$$ in.
Given,
s = 8$$\frac{3}{8}$$ in or 8.3
We know that,
Perimeter of the equilateral triangle = 3a
P = 3 Ã— 8.3
P = 24.9 ft
Thus the perimeter of the equilateral triangle is 24.9 ft

Find the area.

Question 8.
Square with sides of 6.5 cm: ___________
Given,
side = 6.5 cm
We know that,
Area of a square = s Ã— s
A = 6.5 Ã— 6.5
A = 42.25 sq. cm
Thus the area of the square is 42.25 sq. cm

Question 9.
Triangle with base 10 in. and height 6 in.:
Given,
Triangle with base 10 in. and height 6 in
We know that,
Area of triangle = 1/2 Ã— base Ã— height
A = 1/2 Ã— 10 Ã— 6
A = 5 Ã— 6
A = 30 sq. inches

Rectangle with length 3$$\frac{1}{2}$$ ft and width 2$$\frac{1}{2}$$ ft:
Given,
length 3$$\frac{1}{2}$$ ft and width 2$$\frac{1}{2}$$ ft
We know that,
Area of the rectangle = l Ã— w
A = 3$$\frac{1}{2}$$ Ã— 2$$\frac{1}{2}$$
A = $$\frac{7}{2}$$ Ã— $$\frac{5}{2}$$
A = $$\frac{35}{4}$$
Thus the area of the rectangle is $$\frac{35}{4}$$ sq. ft

Visualize Vocabulary

Use the âœ“ words to complete the graphic organizer. You will put one word in each rectangle.

Understand Vocabulary

Complete the sentences using the review words.

Question 1.
A figure larger than the original, produced through dilation, is an ____________
A figure larger than the original, produced through dilation, is an enlargement.

A figure smaller than the original, produced through dilation, is a ____________
A figure smaller than the original, produced through dilation, is a reduction.

Key-Term Fold Before beginning the module, create a key-term fold to help you learn the vocabulary in this module. Write the highlighted vocabulary words on one side of the flap. Write the definition for each word on the other side of the flap. Use the key-term fold to quiz yourself on the definitions used in this module.

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