Free Printable Similar Triangles and Linear Equations

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.

a)

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

b)

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

c)

$y=2x$

d)

$y=3x$

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 $\overline{AE}$ ?

a)

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

b)

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

c)

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

d)

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

3.

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

a)

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

b)

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

c)

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

d)

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

4.

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

a)

x = 10

b)

x = 4

c)

x = 2

d)

x = 5

5.

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

a)

81m

b)

18m

c)

16m

d)

25m

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?

a)

144 feet

b)

72 feet

c)

36 feet

7.

What is the value of x?

a)

9 cm

b)

12 cm

c)

14 cm

d)

16 cm

8.

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

a)

3.75

b)

9.75

c)

10

d)

12

9.

Given that these triangles are similar, what is x?

a)

80

b)

5

c)

4

d)

3

10.

Are the triangles similar?

a)

Yes

b)

No

11.

The 2 shapes are similar. Find x.

a)

2

b)

7

c)

0.5

d)

12

12.

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

a)

The slope of the two triangles are the same.

b)

The triangles are congruent triangles.

c)

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

d)

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

13.

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

a)

Yes, because their slopes both simplify to -6.

b)

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

c)

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

14.

Solve for f.

a)

6

b)

4

c)

3

d)

8

15.

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

a)

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

b)

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

c)

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

d)

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

e)

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

16.

Which of the following is a correct similarity statement for the similar triangles above?

a)

ΔKLM ~ ΔPQR

b)

ΔMLK ~ ΔPRQ

c)

ΔMLK ~ ΔRQP

d)

ΔKLM ~ ΔRQP

e)

ΔLKM ~ ΔRQP

17.

If ΔABC ~ ΔDEF, which side on ΔDEF corresponds with the side length from A to C on ΔABC?

a)

$\overline{FD}$

b)

$\overline{FE}$

c)

$\overline{DE}$

d)

$\overline{EF}$

18.

Which of the following is a correct similarity statement for the similar triangles above? (check all that apply)

a)

ΔABC ~ ΔYZX

b)

ΔBCA ~ ΔZXY

c)

ΔACB ~ ΔYXZ

d)

ΔCBA~ ΔXYZ

e)

ΔBCA ~ ΔXZY

19.

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

a)

True

b)

False

20.

Which of the following statements is true based upon the similarity statement, ΔABC ~ ΔDEF? (check all that apply)

a)

∠ABC ≅ ∠DFE

b)

∠BAC ≅ ∠DEF

c)

∠BAC ≅ ∠EDF

d)

∠BAC ≅ ∠EFD

e)

∠ACB ≅ ∠DFE

Similar Triangles and Linear Equations

Total questions: 20

Worksheet time: 20mins

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