Free Printable Similarity ( Review) Ms. Sanchez 2020

1.

When two triangles are considered similar but not congruent?

a)

The distance between corresponding vertices are equal.

b)

The distance between corresponding vertices are proportionate.

c)

The vertices are reflected across the x-axis.

d)

Each of the vertices are shifted up by the same amount.

2.

Each of the vertices are shifted up by the same amount.

a)

The side lengths and angle measure were multiplied by $\frac{XY}{AB}$

b)

The side lengths were multiplied by $\frac{XY}{AB}$ , while the angle measures were preserved.

c)

The angle measures were multiplied by $\frac{XY}{AB}$ , while the side lengths were preserved.

d)

The angle measures and side lengths were preserved.

3.

$In\ the\ diagram\ below,\ ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹.$
$If𝐴𝐵=6and𝐴𝐶=8,$

which statement will justify similarity by SAS ?

a)

$𝐷𝐸=9,\ 𝐷𝐹=12,\ and∠𝐴≅∠D$

b)

$𝐷𝐸=8,\ 𝐷𝐹=10,\ and∠𝐴≅∠D$

c)

$𝐷𝐸=36,\ 𝐷𝐹=64,\ and∠𝐶≅∠𝐿F$

d)

$𝐷𝐸=15,\ 𝐷𝐹=20,\ and∠𝐶≅∠𝐿F$

4.

Kamal dilates triangle ABC to get triangle A′B′C′. He knows that the triangles are similar because of the definition of similarity transformations. He wants to demonstrate the angle-angle similarity postulate by proving

∠BAC≅∠B′A′C′ and∠ABC≅∠A′B′C′.

a)

Two non-vertical lines have the same slope if and only if they are parallel.

b)

Angles supplementary to the same angle or to congruent angles are congruent.

c)

If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.

d)

If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

5.

Lines AC and FG are parallel. Which statement should be used to prove that triangles ABC and DBE are similar?

a)

Angles BDE and BCA are congruent as alternate interior angles.

b)

Angles BAC and BEF are congruent as corresponding angles.

c)

Angles BED and BCA are congruent as corresponding angles.

d)

Angles BDG and BEF are congruent as alternate exterior angles.

6.

Given the diagram below, what is the value of x?

a)

13.5

b)

14.6

c)

15.5

d)

16.6

7.

A scale model of the Millennium Dome in Greenwich, England, was constructed on a scale of 100 meters to 1 foot. The cable supports are 50 meters high and form a triangle with the cables. How high are the cable supports on the scale model that was built?

a)

0.5 foot

b)

1 foot

c)

1.5 feet

d)

2 feet

8.

Hector knows two angles in triangle A are congruent to two angles in triangle B. What else does Hector need to know to prove that triangles A and B are similar?

a)

Hector does not need to know anything else about triangles A and B.

b)

Hector needs to know the length of any corresponding side in both triangles.

c)

Hector needs to know all three angles in triangle A are congruent to the corresponding angles in triangle B.

d)

Hector needs to know the length of the side between the corresponding angles on each triangle.

9.

In ∆𝑆𝐶𝑈 shown below, points 𝑇 and 0 are on 𝑆𝑈̅̅̅̅ and 𝐶𝑈̅̅̅̅, respectively. Segment 𝑂𝑇̅̅̅̅ is drawn so that ∠𝐶 ≅ ∠𝑂𝑇𝑈.

a)

5.6

b)

8.75

c)

11

d)

15

10.

. In the diagram below, 𝐶𝐷̅̅̅̅ is the altitude drawn to the hypotenuse 𝐴𝐵̅̅̅̅ of right triangle 𝐴𝐵𝐶.

a)

𝐴𝐷 = 2 and 𝐷𝐵 = 36

b)

𝐴𝐷 = 3 and 𝐴𝐵 = 24

c)

𝐴𝐷 = 6 and 𝐷𝐵 = 12

d)

𝐴𝐷 = 8 and 𝐴𝐵 = 17

11.

To find the height of a lamppost at a park, Rachel placed a mirror on the ground 20 feet from the base of the lamppost. She then stepped back 4 feet so that she could see the top of the lamp post in the center of the mirror. Rachel's eyes are 5 feet 6 inches above the ground. What is the height, in feet, of the lamppost?

a)

55 feet

b)

27.5 feet

c)

14.5 feet

d)

7.27 feet

12.

a)

3.2

b)

4.8

c)

16.2

d)

19.2

13.

a)

5

b)

6

c)

7

d)

8

14.

Using the information given below, which set of triangles can not be proven similar?

a)

b)

c)

d)

15.

Which is not a property of all similar triangles?

a)

The corresponding angles are congruent.

b)

The corresponding sides are congruent.

c)

The perimeters are in the same ratio as the corresponding sides.

d)

The altitudes are in the same ratio as the corresponding sides.

16.

$Given\ \Delta ABC∼\Delta DEFsuch\ that\ \frac{AB}{DE}=\frac{3}{2}.\$
$Which\ statement\ is\ not\ true?$

a)

$\frac{BC}{EF}=\frac{3}{2}$

b)

$\frac{m\angle A}{m\angle D}=\frac{3}{2}$

c)

$\frac{area\ of\ \Delta ABC}{area\ of\ \Delta DEF}=\frac{9}{4}$

d)

$\frac{perimeter\ of\ \Delta ABC}{perimeter\ of\ \Delta DEF}=\frac{3}{2}$

17.

a)

12.5

b)

14.0

c)

14.8

d)

17.5

18.

Delroy’s sailboat has two sails that are similar triangles. The larger sail has sides of 10 feet, 24 feet, and 26 feet. If the shortest side of the smaller sail measures 6 feet, what is the perimeter of the smaller sail?

a)

15 ft

b)

36 ft

c)

60 ft

d)

100 ft

19.

The base of an isosceles triangle is 5 and its perimeter is 11. The base of a similar isosceles triangle is 10. What is the perimeter of the larger triangle?

a)

15

b)

21

c)

22

d)

110

20.

Triangle ABC is similar to triangle DEF. The lengths of the sides of ABC are 5, 8, and 11. What is the length of the shortest side of DEF if its perimeter is 60?

a)

10

b)

12.5

c)

20

d)

27.5

Similarity ( Review) Ms. Sanchez 2020

Total questions: 20

Worksheet time: 5hrs 0mins

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