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Unit 7 Review: 6th grade Accelerated
1.
Determine whether the triangles are similar. If so, write a similarity statement.
2.
a. /
b. /
c. /
d. / Not similar
3.On a map, the scale is 1 inch 210 miles. What is the actual distance between two cities if the map distance is 5 inches?
a. / 42 mi / b. / 1,050 mi
c. / 215 mi / d. / 205 mi
4.Ava has a doll house. Her mother wants to make a curtain for the doll’s bed that matches the curtains in Ava’s bedroom. Ava’s curtain is 6 feet long and 3.2 feet wide. The doll’s curtain needs to be 1.5 foot long. How wide will the doll’s curtain be?
a. / ft
b. / ft
c. / ft
d. / ft
5.Mrs. Johnson drew two similar right triangles on the board. The perimeter of the larger triangle is approximately how many times greater than the perimeter of the smaller triangle?
(1 inch ≈ 2.54 centimeters)
a. / 8 times / b. / 7 times
c. / 5 times / d. / 2,888 times
6.Adam wants to create a smaller version of the school flag shown so that the shorter side is 5 feet long. What will be the length of the longer side of the new flag?
Write a proportion, then solve.
Each pair of polygons is similar. Determine the missing side measures.
Write a proportion, then solve.
7.
8.In the figure, triangle ABC is similar to triangle DEC. Determine the distance from point D to point E.
/ a. / 50 yd / b. / 40 yd
c. / 20 yd / d. / 30 yd
9.Two rectangles are similar. The length and width of the first rectangle is 11 meters by 9 meters. The second rectangle is similar by a scale factor 2. What is the area of the second rectangle?
a. / 297 m / b. / 80 m
c. / 396 m / d. / 198 m
10.Triangle has vertices , , and . The triangle is dilated with a scale factor of , and the dilation will be centered at the origin. Write an algebraic representation for the dilation. Determine the coordinates of the image of point E after the dilation.
______
11.On a map, 1 centimeter represents 9 kilometers. The actual distance between Lily’s home and the school is 51.48 kilometers. What is the distance between these locations on the map?
a. / 463.32 cm / b. / 8.58 cm
c. / 5.72 cm / d. / 10.12 cm
Use a problem-solving model to solve each problem.
12.Polygon has vertices , , and . Polygon is dilated using the origin as the center of the dilation. The image is polygon , and has coordinates .
Use the grid shown to draw and find the area of polygon .
a. / 180 sq units / b. / 324 sq units
c. / 144 sq units / d. / 216 sq units
13.Find the vertices of polygon after polygon WXYZ is dilated using the given scale factor.
W(–2, –1), X(–2, 3), Y(0,4), Z(0, 0); scale factor 2
______
14.Callendrew a figure with vertices at coordinatesK(3,6), L(6, 9), M(6, -3), and N(9, -6). Draw Callen's figure anda dilation of that figure with a scale factor of 1/3. What are the coordinates of M?a. (1 , 2) b. (-2, 1)
c.(2, -1) d. (-2, -1)
15.For the pair of similar figures, find the area of the second figure.
What is the scale factor used?______
/
Area =108 / Area =?
16. Determine the distance from the house to the stoplight. Write and solve a proportion for full credit.
Solve each equation using correct steps to both sides.
Check your solution!
17. –13 + q = –40
a. / –27
b. / 27
c. / 520
d. / –53
18. q – 58 = 15
a. / 43
b. / 73
c. / 58
d. / –43
19. 54 = –9x
a. / –6
b. / –0.167
c. / 6
d. / 45
20. = 16
a. / –96
b. /
c. / 10
d. / 22
Answer Key
2.b
3.b
4.d
5.a
6.10.25 ft
7.18.7 in, or 1823 in
8.d
9.c
10.(x , y) ( 34x, 34y)
D¢ (-34 , 3 ) , E¢ (1.5 , 4.5 ) , F¢ ( 6, 2.5 )
11.c
12.d
13.(–4, –2),(–4, 6), (0, 8), (0, 0)
14.c
15.12
The scale factor of the two similar figures is 39, that is 13. The area of the first figure is 108 .
Area of smaller rectangle = area of the larger rectangle (108) x scale factor squared (13)2 = 108 x 19 = 12
So, the area of the smaller rectangle is 12 .
16.10 m; d/5 = 8/4
17.a
18.b
19.a
20.a