Free Printable Review 1 - Topic 5 & 6 Test

1.

$\Delta ABC$ is dilated with the center of dilation at the origin and a scale factor of 3 to obtain $\Delta A'B'C'$ . The triangles corresponding ANGLES are _______________.

a)

similar

b)

congruent

c)

proportional

2.

$\Delta ABC$ is dilated with the center of dilation at the origin and a scale factor of 2 to obtain $\Delta A'B'C'$ . The triangles corresponding SIDES are _______________.

a)

similar

b)

congruent

c)

proportional

3.

$\Delta ABC$ is dilated with the center of dilation at the origin and a scale factor of 0.2 to obtain $\Delta A'B'C'$ . The triangles are _______________.

a)

similar

b)

congruent

c)

proportional

4.

$\Delta ABC$ is dilated with the center of dilation at the origin and a scale factor of 0.5 to obtain $\Delta A'B'C'$ . The triangles corresponding ANGLES are _______________ and their corresponding SIDES are _______________; therefore, the triangles are _______________.

a)

congruent; proportional; similar

b)

congruent; congruent; congruent

c)

proportional; proportional; similar

d)

proportional; congruent; congruent

5.

The line representing the equation x+y=4 is dilated by a scale factor of 1.5, with the center of dilation (4,0). Which statement is true?

a)

The dilated line lies on the original line.

b)

The dilated line is perpendicular to the original line.

c)

The dilated line is parallel to the original line and to its left.

d)

The dilated line is parallel to the original line and to its right.

6.

The line representing the equation x+y=6 is dilated by a scale factor of 1.5, with the center of dilation (0,6). Which statement is true?

a)

The dilated line lies on the original line.

b)

The dilated line is perpendicular to the original line.

c)

The dilated line is parallel to the original line and to its left.

d)

The dilated line is parallel to the original line and to its right.

7.

If $\sin\left(x\right)=\cos\left(x+30\right)$ what is the value of x?

a)

30

b)

60

c)

90

d)

180

8.

If $\sin\left(5x\right)=\cos\left(x+30\right)$ what is the value of x?

a)

10

b)

30

c)

60

d)

90

9.

If $\cos\left(2x-10\right)=\sin\left(3x\right)$ what is the value of x?

a)

10

b)

20

c)

30

d)

90

10.

Pepita has drawn two triangles $\Delta ABC$ and $\Delta A'B'C'$ on the coordinate plane as shown. Which statement is the BEST explanation of the relationship between these triangles?

a)

The given triangles are similar because they can be mapped onto each other by a series of reflections, translations, and dilations.

b)

The given triangles are similar because they can be mapped onto each other by a series of reflections, translations, and rotations.

c)

The given triangles are not similar because they cannot be mapped onto each other by a series of reflections, translations, and dilations.

d)

The given triangles are not similar because they cannot be mapped onto each other by a series of reflections, translations, and rotations.

11.

Pepito has drawn two triangles $\Delta ABC$ and $\Delta A'B'C'$ on the coordinate plane as shown. Which statement is the BEST explanation of the relationship between these triangles?

a)

The given triangles are similar because they can be mapped onto each other by a series of reflections, translations, and dilations.

b)

The given triangles are similar because they can be mapped onto each other by a series of reflections, translations, and rotations.

c)

The given triangles are not similar because they cannot be mapped onto each other by a series of reflections, translations, and dilations.

d)

The given triangles are not similar because they cannot be mapped onto each other by a series of reflections, translations, and rotations.

12.

The rapper named Lil Math Text claims that there are centers of dilations through which a dilation of line n by a factor of 2 leaves line n unchanged. Select all points that represents a center of dilation that supports their claim. Select all that apply. *Hint - if the point is on the line it does not change it

a)

A

b)

B

c)

C

d)

D

e)

E

13.

The rapper named Lil Geo claims that there are centers of dilations through which a dilation of line n by a factor of 2 leaves line n unchanged. Select all points that represents a center of dilation that supports their claim. Select all that apply. *Hint - if the point is on the line it does not change it

a)

A

b)

B

c)

C

d)

D

e)

E

14.

Which equation shows the trigonometric relationship between COMPLEMENTARY angles?

a)

sin(c)=sin(b)

b)

sin(a)=cos(b)

c)

cos(a)=sin(d)

d)

cos(c)=cos(d)

15.

Which equation shows the trigonometric relationship between COMPLEMENTARY angles?

a)

sin(e)=sin(h)

b)

sin(g)=cos(f)

c)

cos(e)=sin(g)

d)

cos(f)=cos(h)

16.

Which trigonometric ratios are equivalent to $\frac{3}{5}$ ? Select ALL that apply.

a)

sin A

b)

cos A

c)

tan A

d)

sin C

e)

cos C

17.

Which trigonometric ratios are equivalent to $\frac{4}{3}$ ? Select ALL that apply.

a)

sin Z

b)

cos Z

c)

tan Z

d)

sin X

e)

tan X

18.

In the figure, $\Delta ABC\sim\Delta JKL$ . Which equation is correct?

a)

$\sin a=\frac{JK}{JL}$

b)

$\sin c=\frac{JK}{KL}$

c)

$\cos a=\frac{JK}{JL}$

d)

$\cos c=\frac{JK}{KL}$

19.

In the figure, $\Delta ABC\sim\Delta XYZ$ . Which equation is correct?

a)

$\sin a=\frac{XY}{XZ}$

b)

$\sin c=\frac{XY}{YZ}$

c)

$\cos a=\frac{XY}{YZ}$

d)

$\cos c=\frac{YZ}{XZ}$

20.

If sin(x) = cos(y), which of these are possible values of x and y?

a)

x=0 and y=0

b)

x=20 and y=70

c)

x=80 and y=100

d)

x=0 and y=60

21.

If sin(x) = cos(y), which of these are possible values of x and y?

a)

x=30 and y=60

b)

x=30 and y=70

c)

x=50 and y=50

d)

x=90 and y=90

22.

Mrs. Gibson dilates the triangle shown below by a scale factor of 4 with the origin as the center to obtain $\Delta A'B'C'$ . Two students wrote the following statements about the triangles.

Student 1: $\Delta ABC$ and $\Delta A'B'C'$ are similar right triangles; therefore, $\cos\left(B\right)=\cos\left(B'\right)$ .

Student 2: $\Delta ABC$ and $\Delta A'B'C'$ are similar right triangles; therefore, $\sin\left(A\right)=\sin\left(A'\right)$ .

a)

only student 1

b)

only student 2

c)

both student 1 and student 2

d)

neither student 1 nor student 2

23.

Mr. Gibson dilates the triangle shown below by a scale factor of 3 with the origin as the center to obtain $\Delta A'B'C'$ . Two students wrote the following statements about the triangles.

Student 1: $\Delta ABC$ and $\Delta A'B'C'$ are similar right triangles; therefore, $\tan\left(B\right)=\tan\left(B'\right)$ .

Student 2: $\Delta ABC$ and $\Delta A'B'C'$ are similar right triangles; therefore, $\sin\left(A\right)=\sin\left(A'\right)$ .

a)

only student 1

b)

only student 2

c)

both student 1 and student 2

d)

neither student 1 nor student 2

24.

Pepito drew segment X'Y' 21 units long on a coordinate plane. Her dilated line segment is parallel to segment XY, which measures 14 units long. What was the scale factor of dilation for the line segment Pepito drew? *Hint scale factor is written new length to old length*

a)

$\frac{3}{2}$

b)

$\frac{2}{3}$

c)

$\frac{1}{3}$

d)

$\frac{5}{3}$

25.

Pepito drew segment X'Y' 10 units long on a coordinate plane. Her dilated line segment is parallel to segment XY, which measures 6 units long. What was the scale factor of dilation for the line segment Pepito drew? *Hint scale factor is written new length to old length*

a)

$\frac{3}{5}$

b)

$\frac{3}{2}$

c)

$\frac{1}{3}$

d)

$\frac{5}{3}$

26.

Given point $A\left(2,\ -6\right)$ and point $B\left(8,4\right)$ on directed line segment AB, what is the y-coordinate of Point F that partitions AB in the ratio of $3:2$ ?

a)

-2

b)

0

c)

5

d)

6

27.

Given point $A\left(1,\ -8\right)$ and point $B\left(9,7\right)$ on directed line segment AB, what is the y-coordinate of Point F that partitions AB in the ratio of $3:2$ ?

a)

1

b)

15

c)

5

d)

10

28.

The length of segment CD is 14 units. Segment C'D' is the image of segment CD under a dilation with a scale factor of n. Which of these are true? Choose all that are correct. *Hint scale factor is written new length to old length*

a)

If $n=\frac{3}{2}$ segment C'D'=21 units

b)

If n=3, segment C'D'=5 units

c)

If n=2, segment C'D'=28 units

d)

If n=5, segment C'D'=30 units

e)

If $n=\frac{1}{2}$ , segment C'D'=7 units

29.

The length of segment CD is 25 units. Segment C'D' is the image of segment CD under a dilation with a scale factor of n. Which of these are true? Choose all that are correct. *Hint scale factor is written new length to old length*

a)

If $n=\frac{3}{2}$ segment C'D'=20 units

b)

If n=3, segment C'D'=75 units

c)

If n=4, segment C'D'=50 units

d)

If $n=\frac{1}{5}$ , segment C'D'=5 units

e)

If $n=\frac{8}{5}$ , segment C'D'=40 units

30.

If $\Delta ABC\$ is similar to $\Delta DEF$ , determine the measure of $\angle A$ .

a)

$18\degree$

b)

$60\degree$

c)

$26\degree$

d)

$8\degree$

31.

If $\Delta ABC\$ is similar to $\Delta DEF$ , determine the measure of $\angle A$ .

a)

$90\degree$

b)

$38\degree$

c)

$28\degree$

d)

$18\degree$

32.

What is the measure of angle $\theta$ ?

a)

$66.4\degree$

b)

$23.6\degree$

c)

$21.8\degree$

d)

$68.2\degree$

33.

What is the measure of angle $\theta$ ?

a)

$70.5\degree$

b)

$18.4\degree$

c)

$71.6\degree$

d)

$19.5\degree$

34.

Which equation could be used to find the height of the flagpole?

a)

$\sin\left(60\right)=\frac{x}{20}$

b)

$\cos\left(60\right)=\frac{x}{30}$

c)

$\tan\left(60\right)=\frac{x}{20}$

d)

$\sin\left(30\right)=\frac{20}{x}$

35.

Which equation could be used to find the height of the flagpole?

a)

$\tan\left(50\right)=\frac{x}{10}$

b)

$\cos\left(50\right)=\frac{x}{10}$

c)

$\tan\left(40\right)=\frac{x}{10}$

d)

$\cos\left(40\right)=\frac{x}{10}$

Review 1 - Topic 5 & 6 Test

Total questions: 35

Worksheet time: 2hrs 49mins

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