Quiz about Similar Triangles and Linear Equations

Question 1

On the coordinate plane in the image, triangle PQR is similar to triangle RST. The corresponding side lengths of triangle RST and triangle PQR are in the ratio of 3:1. What is the equation of the line containing the points P and T.

Accepted Answer

$$y=2x$$

Answer

$$y=\frac{2}{3}x$$

Answer

$$y=\frac{3}{2}x$$

Answer

$$y=3x$$

Question 2

Two similar triangles $$\Delta ABC$$ and $$\Delta EDC$$ are shown in the image. Which of these proportions has ratios that are equal to the slope of $$\overline{AE}$$ ?

Accepted Answer

$$\frac{BC}{AB}=\frac{CD}{DE}$$

Answer

$$\frac{AB}{CD}=\frac{DE}{BC}$$

Answer

$$\frac{AB}{DE}=\frac{BC}{CD}$$

Answer

$$\frac{BC}{AC}=\frac{CD}{CE}$$

Question 3

Which of the following statements is TRUE of triangles FGH and HJK in the image.

Accepted Answer

Because FGH and HJK are similar, the slope is the same between any 2 distinct points on the line

Answer

The absolute value of the slope of the line is equal to $$\frac{HJ}{FG}$$

Answer

The absolute value of the slope is equal to $$\frac{FG}{JK}$$

Answer

Because FGH and HJK are not similar, the slope is found by using 2 distinct points on one of the triangles.

Question 4

The pair of figures is similar. Find the missing side.

Accepted Answer

x = 10

Answer

x = 4

Answer

x = 2

Answer

x = 5

Question 5

The two triangles are similar. Find the distance d across the river?

Accepted Answer

25m

Answer

81m

Answer

18m

Answer

16m

Question 6

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. How tall is the tree?

Accepted Answer

72 feet

Answer

144 feet

Answer

36 feet

Question 7

What is the value of x?

Accepted Answer

12 cm

Answer

9 cm

Answer

14 cm

Answer

16 cm

Question 8

The two right triangles below are similar. What is x, the missing side length in triangle DEF?

Accepted Answer

9.75

Answer

3.75

Answer

10

Answer

12

Question 9

Given that these triangles are similar, what is x?

Accepted Answer

5

Answer

80

Answer

4

Answer

3

Question 10

Are the triangles similar?

Accepted Answer

Yes

Answer

No

Question 11

The 2 shapes are similar. Find x.

Accepted Answer

7

Answer

2

Answer

0.5

Answer

12

Question 12

Which of the following statements is true about the triangles shown on the graph?

Accepted Answer

The slope of the two triangles are the same.

Answer

The triangles are congruent triangles.

Answer

The slope of the larger triangle is larger than the slope of the smaller triangle.

Answer

The slope of the smaller triangle is smaller than the slope of the larger triangle.

Question 13

Explain whether or not the triangles shown could lie on the same line.

Accepted Answer

Yes, because their slopes both simplify to -6.

Answer

Yes, because their slopes both simplify to 1/6.

Answer

No, because -72/12 is not the same as -144/24

Question 14

Solve for f.

Accepted Answer

4

Answer

6

Answer

3

Answer

8

Question 15

Which of the following equations could correctly apply to the similar triangles below? (check all that apply)

Accepted Answer

$$\frac{a}{c}=\frac{b}{d}$$

Accepted Answer

$$\frac{a}{b}=\frac{c}{d}$$

Accepted Answer

$$\frac{c}{a}=\frac{d}{b}$$

Answer

$$\frac{a}{d}=\frac{b}{c}$$

Answer

$$\frac{d}{c}=\frac{a}{b}$$

Question 16

True or False: On similar figures, each pair of corresponding sides have a common ratio for their lengths.

Accepted Answer

True

Answer

False

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