Unit 5

review

QUESTION 1

A transformation where a geometric figure is reduced or enlarged in the coordinate plane is called a _____________________

#1 - answer

Dilation

QUESTION 2

Figures that are exactly the same size and the same shape are ________________ figures.

#2 - answer

congruent

QUESTION 3

List the characteristics of similar figures.

#3 - answer

*same shape

*corresponding angles are congruent

*corresponding sides are proportional

QUESTION 4

One vertex of a triangle on the coordinate plane has the ordered pair of (32, 16). The rectangle undergoes a ¼ dilation. What would be the new coordinates of the corresponding vertex?

#4 - answer

(8, 4)

Question 5

• Cheryl wants to dilate a photograph that has a width of 17.5 inches and a length of 24.5 inches to fit into a frame that is 7 inches in length. What will be the width of the new photograph?

#5 - answer

5 inches

You can set up a proportion. Or, you can divide 24.5 by 7, which equals 3.5. Then, divide 17.5 by 3.5.

Question 6

• Stacey decides to dilate the area of her rectangular garden. The length of her original garden is 10 feet and the area is 45 square feet. The length of the new garden will be 15 feet. What is the area of the new garden?

#6 - answer

101.25 ft²

A = 45 ft²

10 ft 15 ft

A = 101.25 ft²4.5 ft 6.75 ft

Scale Factor = 1.5Area Scale Factor = 2.25

Question 7Find the value of x if triangle ABC ~ triangle

JPHA

BC

J

PH12

15

66

x

#7 - answer

• X = 82.5

Question 8• Determine the scale factor of the first

figure to the second figure.

7 in 11 in

#8 - answer

11/ 7 in

Question 9

State whether the dilation would be reduced, enlarged, or congruent.

Scale factor = 1/17

#9 - answer

reduced

Question 10

State whether the dilation would be reduced, enlarged, or congruent.

Scale factor = 17

#10 - answer

enlarged

Question 11

• A vertex of a rectangle on the coordinate plane is (-4, -2). The rectangle is dilated and the new coordinate of the vertex is

(-2, -1). What was the scale factor of the dilation?

#11 - answer

1/2

Question 12

State whether the dilation would be reduced, enlarged, or congruent.

Scale factor = 1

#12 - answer

congruent

Question 13If triangle ABC ~ triangle JPH. Which

proportion can be used to find the value of x? A

BC

J

PH12

15

66

x

#13 - answer

Question 14

Determine the scale factor from the reduction of the first figure to the second figure.

53

#14 - answer

3

5

Question 15

Find the area of the smaller similar rectangle.

16

8

4

x

#15 - answer

Area = 8

*scale factor is 4/16 or ¼. 8 times ¼ = 2. Therefore, x = 2.

Area = length times width

8 = 2 • 4

Question 16

Find the area of the larger similar rectangle.

14

x

4

5

#16 - answer

Area = 245

14 ÷ 4 = 3.5

x = 5 • 3.5

x = 17.5

17.5 • 14 = 245

Question 17

If rectangle ABCD ~ rectangle WXYZ, what side corresponds with YZ?

#17 - answer

CD

Question 18

Rectangle ABCD ~ rectangle WXYZ.

Is WX congruent to BC?

#18 - answer

No

Question 19

Are all squares similar?

#19 - answer

Yes

Question 20

A flagpole is 28 ft tall and has a shadow of 20 ft. How tall is a nearby tree if its shadow is 30 ft?

#20 - answer

42 feet

Question 21

Triangle ABC ~ to triangle WXY. Use the diagram to find the perimeter of triangle ABC.

A

B C

W

X Y

5 m

3 m

4 m

21 m

#21 - answer

The area of the large triangle is 84 m.

*3 • 7 = 21 Therefore, the scale factor is 7.

4 • 7 = 28 and 5 • 7 = 35.

Add the sides of the large triangle to get the perimeter. 28 + 35 + 21 = 84 m.

Question 22

x in

7 in

12 in

21 in

#22 - answer

x = 4 in

Question 23

One vertex of a triangle on the coordinate plane has the ordered pair of (24, 16). The triangle undergoes 1/8 dilation. What would be the new coordinates of the corresponding vertex?

#23 - answer

(3, 2)

Question 24

• Brooke is 5 ft tall. She and her class are walking through a wooded area looking for a tree that is 50 ft. tall. If the length of Brooke’s shadow is 2 ft, how will the students know when they have found a 50 ft tree?

#24 - answer

• When they find a tree’s shadow that measures 20 feet.

Question 25

• A shrub is 1.5 meters tall and casts a shadow 3.5 meters long. At the same time, a radio tower casts a shadow 98 meters long. How tall is the radio tower?

#25 - answer

42 meters

Question 26

Linda wants to enlarge a 5 inch by 7 inch photograph that will fit into a frame that is 21 inches long. What is the width of the new photograph?

#26 - answer

• 15 inches

7 in

5 in

21 in

21/7 = 3 (scale factor)

5 • 3 = 15