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similar shapes

Total questions: 16

Worksheet time: 15mins

Name
Class
Date
1.
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
2.
Are the two figures similar?
a)
yes
b)
no
3.
Are these triangles similar?
a)
Yes
b)
No
4.

Which scale factor shrinks a figure?

a)

k = 0

b)

k =2

c)

k= 1/3

d)

k = 1

5.
Which transformation(s) create(s) similar figures?
a)
Dilation
b)
Translation, Reflection, and Rotation
c)
Translation and Reflection
d)
Reflection and Rotation
6.
Tell whether the two figures are similar. Explain your reasoning.
a)
Yes, similar because they are the same shape and side lengths are proportional.
b)
No, not similar because they are the same shape, but side lengths are not proportional.
c)
Yes, same shape
d)
No, different sizes
7.
A pentagon graphed on a coordinate plane underwent a rotation about the origin, a reflection across the y–axis, a translation down, and a dilation with a scale factor of 3 from its center to produce another pentagon. Which of these statements is true about the original pentagon and the new pentagon?
a)
They are similar.
b)
They may or may not be similar, depending on the number of units translated.
c)
They may or may not be similar, depending on the number of degrees rotated.
d)
They are not similar.
8.

Quad OBCD is similar to Quad OHTE because:

a)

Quad OBCD can be reflected over the x axis and then rotated 90 degrees

b)

Quad OBCD can be reflected over the x-axis and then dilated about point O by a scale factor of 2.

c)

Quad OBCD can be reflected over the y-axis and then dilated about point O by a scale factor of 2.

d)

Quad OBCD can be reflected over the y-axis and then dilated about point O by a scale factor of 1/2.

9.
All angles in similar figures are congruent.  
a)
True
b)
False
10.

If in ▲ DEF and ▲ PQR, D = Q, R = E then which of the following statements is false ?

a)

EFPR = DFPQ\frac{EF}{PR}\ =\ \frac{DF}{PQ}

b)

DEPQ = EFRP\frac{DE}{PQ}\ =\ \frac{EF}{RP}

c)

DEQR = DFPQ\frac{DE}{QR}\ =\ \frac{DF}{PQ}

d)

EFRP = DEQR\frac{EF}{RP}\ =\ \frac{DE}{QR}

11.

Which statement is true in similarity

a)

Every equilateral triangle is similar and congruent

b)

Every equilateral triangle is similar but their sides are not in proportion

c)

Every Equilateral triangle is congruent but not similar

d)

Two congruent triangles are similar

12.

What is the distance from X to the rock, if the triangle are similar?

a)

30 feet

b)

40 feet

c)

50 feet

d)

63 feet

13.

ABCD ~ WXYZ. AD = 12, DC = 6, and WZ = 35. Find YZ. The figures are not drawn to scale. Label the figures.

a)

17.5

b)

210

c)

7.8

d)

70

14.

Triangle MRT is similar, but not congruent, to triangle ABC. Triangle ABC underwent two transformations to get Triangle LMN. Select two of the following pairs of transformations that could have occurred.

a)

Dilation of 1/2 and a translation of 8 units down

b)

90-degree counterclockwise rotation and a dilation of 3.

c)

Translations of 5 units down and left and a reflection over the x-axis

d)

Reflection over y=3x+5 and a 180 degree clockwise rotation.

15.

The triangles are similar. Solve for x.

a)

4

b)

5

c)

6

d)

7

16.

Which proportion is true?

a)

vw=54.38\frac{v}{w}=\frac{5}{4.38}

b)

v6=4.22.52\frac{v}{6}=\frac{4.2}{2.52}

c)

6w=57.3\frac{6}{w}=\frac{5}{7.3}

d)

v6=7.32.52\frac{v}{6}=\frac{7.3}{2.52}