This handy Math in Focus Grade 8 Workbook Answer Key Chapter 9 Congruence and Similarity detailed solutions for the textbook questions.

## Math in Focus Grade 8 Course 3 B Chapter 9 Answer Key Congruence and Similarity

### Math in Focus Grade 8 Chapter 9 Quick Check Answer Key

**Complete.**

Question 1.

Answer:

Explanation:

1. Scale factor: 2

2 × 8ft = 16 ft

2. Original length = 5

Scaled length = 5

Scale factor = 5/5 = 1

3. Original length = 8 m

Scaled length = 4 m

Scale factor = scale/actual = 4/8 = 1/2

4. Scale factor = 1/4

Original length = 4 inches

We know that

scale factor = scale/actual

1/4 = scale length/4

scaled length = 4/4

scaled length = 1 in.

**Solve.**

Question 2.

Shawn built a model of a ship whose length was 4,500 inches. His model was 15 inches long. Find the scale factor.

Answer:

Let the scale factor be x

Shawn built a model of a ship whose length was 4,500 inches.

His model was 15 inches long.

x × 15 = 4500

x = 4500/15

x = 300 inches

Question 3.

A line segment is 4 centimeters long. When projected on a screen, the line segment is 20 centimeters long. Find the scale factor.

Answer:

Let the scale factor be x

scale factor = scale/actual

Actual length = 4 cm

scaled length = 20 cm

scale factor = 20 cm/4 cm

scale factor = 5 cm

Thus the scale factor is 5 cm.

Question 4.

A model plane is built with a scale factor of \(\frac{1}{180}\). The actual length of the plane is 210 feet (2,520 inches). Find the length of the model.

Answer:

Given,

A model plane is built with a scale factor of \(\frac{1}{180}\).

The actual length of the plane is 210 feet (2,520 inches).

Scale/Actual = 1/180

1/180 = l/210 feet

210/180 = length

Length = 210/180

Length = 21/18

Length = 7/6

Length = 1.16 feet

Question 5.

The scale of a map is 2 inches : 3 kilometers. The length of a road on the map is 3 inches. Find the actual length of the road.

Answer:

Given,

The scale of a map is 2 inches : 3 kilometers.

The length of a road on the map is 3 inches

Let the actual length of the road be x.

2 in./ 3 km = 3 in / x km

x = (3 × 3)/2

x = 9/2 = 4.5 km

Thus the actual length of the road is 4.5 kilometers.

Question 6.

The diagram shows a plot of land ABCD drawn on a map.

a) On the map, \(\overline{C D}\) is 1\(\frac{3}{4}\) inches. Find the scale of the map.

Answer:

b) Find the area of ABCD on the map.

Answer:

**The measures of two interior angles are given for each triangle. Find the measure of the third interior angle.**

Question 7.

△ABC: 20°, 80°

Answer:

Given

△ABC: 20°, 80°

The sum of interior angles of the triangle = 180°

∠a + ∠b + ∠c = 180°

20°+ 80° + ∠c = 180°

100° + ∠c = 180°

∠c = 180° – 100°

∠c = 80°

Thus the measure of the third interior angle is 80°

Question 8.

△KLM: 37°, 76°

Answer:

Given,

△KLM: 37°, 76°

The sum of interior angles of the triangle = 180°

∠k + ∠l + ∠m = 180°

37°+ 76° + ∠m = 180°

113° + ∠m = 180°

∠m = 180° – 113°

∠m = 67°

Thus the measure of the third interior angle is 67°

Question 9.

△PQR: 15°, 103°

Answer:

Given,

△PQR: 15°, 103°

The sum of interior angles of the triangle = 180°

∠p + ∠q + ∠r = 180°

15°+ 103° + ∠r = 180°

∠r = 180° – 118°

∠r = 62°

**Find the unknown angle measure.**

Question 10.

Answer:

Let the unknown angle be y

The sum of three angles = 180°

20° + 27° + y = 180°

47° + y = 180°

y = 180° – 47°

y = 133°

x° + y° + 27° = 180°

x° + 133° + 27° = 180°

x° = 180° – 133° – 27°

x° = 20°

Thus the unknown angle is 20°

Question 11.

Answer:

y° + y° = 120°

2y° = 120°

y = 120°/2

y =60°

**Solve for each variable.**

Question 12.

Answer:

a° + 2b° = 180

b° = 40° (alternate angles)

2b° = 80°

a° + 2b° = 180

a° + 80° = 180°

a° = 180° – 80°

a° = 100°

Question 13.

Answer:

c° + 28° = 180°

c° = 180° – 28°

c° = 152°