AnswersCA-Math 8 BSimilar Triangles and Slope

Similar Triangles and Slope Answers

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1
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Given k l, what can you conclude about these triangles? Check all that apply.

Question illustration
A
Vertical angles prove 1 4.
Option A
B
Alternate exterior angles prove 5 3.
Option B
C
5 and 3 are alternate interior angles.
Option C
D
The ratios of the corresponding angles are equivalent.
E
The triangles are similar because all corresponding angles are congruent.
2
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What is the ratio of the rise to the run in the larger triangle in the diagram? y/xx/y✔ (y – 3)/x x/(y – 3)

A
y/x
B
x/y
C
✔ (y – 3)/x
D
x/(y – 3)
3

What is the equation of the line in slope-intercept form? ✔ y = (2/3)x + 3y = 2x + 3y = (2/3)x – 3 y = 2x – 3

A
✔ y = (2/3)x + 3
B
y = 2x + 3
C
y = (2/3)x – 3
D
y = 2x – 3
4

Which statement is true based on the diagram?

A
PQR ~ STR
Option A
B
RST ~ RQP
Option B
C
QR corresponds to TR.
Option C
D
PR corresponds to RS.
Option D
5

What is the value of x?

Answer:

12

6

The distance between the lions and the monkeys is feet.

Answer:

64

7

The path from the whales to the sharks is parallel to the path from the penguins to the stingrays. What is the distance between the penguins and the stingrays?

A
feet
Option A
B
28 feet
Option B
C
45 feet
Option C
D
63 feet
Option D
8

Is Julia correct? If not, what was her mistake?

A
Yes, she is correct.
B
No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios.
C
No, she needed to have the product of the numerators equal to the product of the denominators.
D
No, she needed to multiply 7.5 to both sides.
9

Use the similar triangles on the coordinate plane to determine the equation for the given line.

A
Option
Option A
B
Option
Option B
C
y = 4x + 3
Option C
D
y = 3x + 4
Option D
10

Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3).

Answers:
Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3).:2/3
Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3).:(y – 3)/x
Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3).:y = (2/3)x + 3
11

Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3). What is the ratio of the rise to the run in the smaller triangle in the diagram? What is the ratio of the rise to the run in the larger triangle in the diagram? What is the equation of the line in slope-intercept form?

Answers:
Selection 1:2/3
Selection 2:(y – 3)/x
Selection 3:y = (2/3)x + 3
12

Given k l, what can you conclude about these triangles? Check all that apply.

Question illustration
A
Vertical angles prove 1 4.
Option A
B
Alternate exterior angles prove 5 3.
Option B
C
5 and 3 are alternate interior angles.
Option C
D
The ratios of the corresponding angles are equivalent.
E
The triangles are similar because all corresponding angles are congruent.
13

Which statement is true based on the diagram?

A
PQR ~ STR
Option A
B
RST ~ RQP
Option B
C
QR corresponds to TR.
Option C
D
PR corresponds to RS.
Option D
14

What is the value of x?

Answer:

12

15

The distance between the lions and the monkeys is feet.

Answer:

64

16

The path from the whales to the sharks is parallel to the path from the penguins to the stingrays. What is the distance between the penguins and the stingrays?

A
feet
Option A
B
28 feet
Option B
C
45 feet
Option C
D
63 feet
Option D
17

Is Julia correct? If not, what was her mistake?

A
Yes, she is correct.
B
No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios.
C
No, she needed to have the product of the numerators equal to the product of the denominators.
D
No, she needed to multiply 7.5 to both sides.
18

Use the similar triangles on the coordinate plane to determine the equation for the given line.

A
Option
Option A
B
Option
Option B
C
y = 4x + 3
Option C
D
y = 3x + 4
Option D
19

Which did you include in your response?

A
I would need to know the length of a pair of corresponding sides.
B
I would set up a proportion.
C
I would put corresponding measures from the triangles in the same position in the ratios.
D
Then I would cross-multiply to solve.
20

What is the ratio of the rise to the run in the smaller triangle in the diagram? ✔ 2/33/22/13/1

A
2/3
B
3/2
C
2/1
D
3/1

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