Review Geometry Chapter 7 Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. What characteristics do similar triangles have?
A. equal angles and sides in the same ratio. C. equal perimeter
B. equal area D. equal size
____ 2. Which proportion is NOT correct?
E
A
S
15
o15
oT
A. ET
ST EA
AS C.
ET EA
ST AS
____ 3. Which similarity statement is true for the triangles shown?
E
G R
X
Y
Z 5
6 7
18
21 15
A. EGR YZX C. EGR XYZ
B. EGR XZY D. EGR YXZ
____ 4. What is a similarity transformation?
A. A transformation similar to the previous one.
C. A composite of one or more dilations and one or more congruence transformations. B. A composite of translations that only act
on similar triangles.
D. A transformation that makes all parallelograms into similar rectangles.
____ 5. The dilation D:xy 2x,4y has been applied to the polygon S1,1, T1,1, U0,3. What are the
coordinates of the image points?
A. S2,4,T4,4,U3,6 C. S 2,4,T2,4,U0,12
B. S 1,1,T1,1,U0,3 D. S 4,2,T 2,2,U 3,0
____ 6. Polygon KLMN was mapped to polygon OPQR. To perform the mapping, the dilation: x,y 2x,4y and
the translation: x,y x1,y2 were used. Is OPQR similar to KLMN?
____ 7. Which similarity postulate or theorem lets you conclude that JKL MNO?
A. SSS C. AAS
B. AA D. SAS
____ 8. ABC had vertices A0,0, B10,0, and C0,8. Which set of coordinates can be used to prove
ABC DEF?
A. D0,0,E5,0,F0,4 B. D0,0,E0,5,F4,0
____ 9. A video game designer is modeling a tower that is 320 ft high and 300 ft wide. She creates a model so that the similarity ratio of the model to the tower is 4001 . What is the height and the width of the model in inches?
A. height = 0.8 in.; width = 0.75 in.
B. height = 128,000 in.; width = 120,000 in. C. height = 9.6 in.; width = 9 in.
____ 10. Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points.
D: (x,y) (3.5x,3.5y)
J(1, 4), K(6, 4), L(6, 1), M(1, 1)
A. J´(3.5, 14), K´(21, 14),
L´(21, 3.5), M´(3.5, 3.5)
C. J´(14, 3.5), K´(14, 21),
L´(3.5, 21), M´(3.5, 3.5) B. J´(3.5, 14), K´(21, 14),
L´(6, 1), M´(1, 1)
D. J´(–3.5, –14), K´(–21, –14),
L´(–21, –3.5), M´(–3.5, –3.5)
____ 11. Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points. Identify and describe the transformation.
D: (x,y) (4x,4y)
A(2, 1), B(4, 1), C(4, 3)
A. This is a dilation about (0, 0) with a scale factor of 0.25; A’(8, 4), B’(16, 4), C’(16, –12). B. This is a dilation about (0, 0) with a scale factor of 4; A’(8, 4), B’(16, 4), C’(16, –12). C. This is a dilation about (0, 0) with a scale factor of 0.25; A’(0.5, 0.25), B’(1, 0.25), C’(1,
–0.75).
____ 12. Determine whether the polygons with the given vertices are similar. Quadrilateral ABCD with vertices A(–4, 5), B(–2, 5), C(–2, 4), D(–4, 4) and quadrilateral EFGH with vertices E(0, 0), F(8, 0), G(8, –4), H(0, –4) A. The polygons are not similar.
ABCD can be mapped onto A’B’C’D’ by a translation: (x,y) (x4,y5). But A’B’C’D’ cannot be mapped onto EFGH by a dilation.
B. The polygons are similar.
ABCD can be mapped onto A’B’C’D’ by a translation: (x,y) (x4,y5). Then A’B’C’D’ can be mapped onto EFGH by a dilation: (x, y)-->(4x, 4y).
C. The polygons are not similar.
ABCD can be mapped onto A’B’C’D’ by a translation: (x,y) (x5,y4). But A’B’C’D’ cannot be mapped onto EFGH by a dilation.
D. The polygons are similar.
ABCD can be mapped onto A’B’C’D’ by a translation: (x,y) (x5,y4). Then A’B’C’D’ can be mapped onto EFGH by a dilation: (x, y)-->(4x, 4y).
____ 13. Prove that circle A with center (–3, 1) and radius 3 is similar to circle B with center (2, –1) and radius 5. A. Circle A can be mapped to circle A’ by a translation (x,y) (x5,y2). Then circle A’
can be mapped to circle B by a dilation with scale factor 5 3. So, circles A and B are similar.
B. Circle A can be mapped to circle A’ by a translation (x,y) (x2,y5). Then circle A’
can be mapped to circle B by a dilation with scale factor 3 5. So, circles A and B are similar.
C. Circle A can be mapped to circle A’ by a translation (x,y) (x5,y2). Then circle A’
can be mapped to circle B by a dilation with scale factor 3 5. So, circles A and B are similar.
D. Circle A can be mapped to circle A’ by a translation (x,y) (x2,y5). Then circle A’
____ 14. Find NP.
A. NP = 1 C. NP = 1.6
B. NP = 1.25 D. NP = 2
____ 15. A tree is standing next to a 40-foot high building. The tree has an 18-foot shadow, while the building has a 16-foot shadow. How tall is the tree, rounded to the nearest foot?
A. 45 feet C. 42 feet
B. 36 feet D. 7 feet
____ 16. Given ABC JKL, find the perimeter and area of JKL.
____ 17. MNOP is a parallelogram. Find MP.
A. MP = 25 C. MP = 20
B. MP = 30 D. MP = 6
Numeric Response
18. If 8, 14, and 16 and 12, 21, and x are the lengths of the corresponding sides of two similar triangles, what is the value of x?
19. PQ with endpoints P(4,4) and Q(7,8) is dilated by a scale factor of 6. Find the length of P'Q'.
Short Answer
20. If the triangles below are congruent, justify with a triangle congruence theorem and indicate corresponding vertices. Otherwise, write "not enough information to know."
A B
C D
21. WXZ VXY. If VY = 5, WX =13 , and VX =6 , find WZ to the nearest tenth.
X
Y
Z W
V
22. Which value of x makes the two rectangles similar?
30
100
2
x
23. A room has the dimensions shown. A scale drawing of the room is actually 2 in. tall. What is the width of the scale drawing?
25 ft
60 ft
24. What is the length of YZ ?
E
G
R
X
Y
Z
27
30
18
20
15
25. TS
PR
. What is the length of QS?
P
Q
R
T
S
27
30
15
26. The scale on a map is 2.5 cm : 1150 m. If the distance between the school and the library on the map is 14 centimeters, what is the actual distance between the buildings?
27. Which coordinates for V make SOT UOV?
28. A community is building a square park with sides that measure 150 meters. To separate the picnic area from the play area, the park is split by a diagonal line from opposite corners. Determine the approximate length of the diagonal line that splits the square. If necessary, round your answer to the nearest meter.
29. Find the point P along the directed line segment from point A(–6, 1) to point B(13, 13) that divides the segment in the ratio 4 to 7.
Review Geometry Chapter 7 Test
Answer Section
MULTIPLE CHOICE 1. A
2. B 3. D 4. C 5. C 6. A 7. B 8. A 9. C
Step 1 Convert measurements to inches. tower’s length 320 ft 3840 in. tower’s width 300 ft 3600 in.
Step 2 Apply the scale factor formula.
new dimension = (scale factor)(original dimension)
model’s length 4001
3840 in.9.6 in.
model’s width 4001
3600 in.9 in.
10. A 11. B 12. B 13. A 14. B
It is given that PR NQ, so PN
NM RQ
QM by the Triangle Proportionality Theorem. PN
5 2
8 Substitute 2 for RQ, 8 for QM, and 5 for NM. 8(PN)10 Cross Products Property
15. A
Because the sun’s rays are parallel, we know that J C. Therefore ABC GHJ by AA similarity.
The height of the tree is the length of GH.
AB AC
GH
GJ Corresponding sides are proportional.
40 16
GH
18 Substitute.
(40)(18)16(GH) Cross Products Property 45GH Divide both sides by 16.
The height of the tree is 45 feet. 16. A
For the two triangles the similarity ratio is 1812, or 32.
By the Proportional Perimeters and Areas Theorem, the ratio of the triangles’ perimeters is also 32, and the
ratios of their areas is 32
2
9
4. Perimeter:
P
28 3
2 Set up the ratio.
2(P)(28)(3) Cross Products Property
P42 feet Simplify.
Area:
17. B
MP NO Opposite sides of a parallelogram are congruent. MP = NO Definition of congruent segments
5x3x12 Substitute.
x6 Simplify and solve.
MP = 5x = 5(6) = 30 Substitute and solve for entire segment measure.
NUMERIC RESPONSE 18. 24
19. 30
SHORT ANSWER
20. HL Congruence Theorem; ABE CDE
21. 10.8
22. 62 3
23. 5 6 in. 24. 10
25. 162 3 26. 6440 m 27. 12,0
28. 212 m
29. P(10 11,
59 11)
30. P(36 11,
