accelerated grade 7 module 1 assessments

Accelerated Grade 7

Module 1 Assessments

Student Edition

G8_FM_SE.indd 1 6/3/21 9:34 PM

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RIGID MOTION TRANSFORMATIONS: Standardized Test • 1

RIGID MOTION TRANSFORMATIONS

End of Topic AssessmentName Date

1. Logan drew ∆ ABC on the coordinate plane, and then reflected the triangle over the y -axis to form ∆ A′B′C′ . Which statement is NOT true about these two triangles?

a. Triangle ABC is congruent to triangle A′B′C′.

b. The two triangles have the same angle measures.

c. The vertices of ∆ ABC and ∆ A′B′C′ have the same coordinates.

d. The triangles have the same side lengths.

2. Blake drew square ABCD . Then, he drew the image of it, square A′B′C′D′ , 2 centimeters to the right of the original figure. Line segment BC is 3 centimeters. How long is line segment B′C′?

a. 1 cm

b. 3 cm

c. 5 cm

d. 6 cm

3. Dianne drew a triangle with coordinates (1, 3) , (3, 2) , and (4, 2) . She drew an image of the triangle with coordinates (− 1, 3) , (− 3, 2) , and (− 4, 2) . How did she make the image?

a. (x, y) → (–x, y)

b. (x, y) → (x, –y)

c. (x, y) → (x – 2, y)

d. (x, y) → (x, y – 2)

4. Regina drew a triangle with vertices at (1, 2), (3, 3), and (4, 1). She slides the triangle 2 units down to create an image. What are the vertices of the image?

a. (1, 0) , (3, 1) , and (4, −1)

b. (1, 4) , (3, 5) , and (4, 3)

c. (−1, 2) , (1, 3) , and (2, 1)

d. (3, 2) , (5, 3) , and (6, 1)

AccG7_M01_T01_Assessment.indd 1 7/27/21 12:40 PM

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2 • MODULE 1: Transforming Geometric Objects


5. Tasha traces her protractor on a piece of graph paper. Then, she holds one corner of the protractor still while she turns the rest of the protractor 90° clockwise. Finally, she traces the protractor again. What type of transformation did Tasha perform?

a. duplication

b. translation

c. reflection

d. rotation

6. Parallelogram GHIJ is rotated 180° about the origin to form parallelogram G’H’I’J’.

Which statement is true?

a. The sum of the angle measures of parallelogram GHIJ are 180° more than the sum of the angle measures of parallelogram G’H’I’J’.

b. The angle measures of parallelogram GHIJ are equal to the corresponding angle measures of parallelogram G’H’I’J’.

c. Parallelogram GHIJ is not congruent to parallelogram G’H’I’J’.

d. The sum of the angle measures of parallelogram GHIJ is 180° less than the sum of the angle measures of parallelogram G’H’I’J’.


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7. Samantha drew ∆ JKL with the coordinates (2, 3) , (4, 3) , and (5, 2) . She reflected this triangle over the x-axis to create an image. What are the coordinates of the image?

a. (0, 3) , (2, 3) , and (3, 2)

b. (2, 0) , (4, 0) , and (5, −1)

c. (−2, 3) , (−4, 3) , and (−5, 2)

d. (2, −3) , (4, −3) , and (5, −2)

8. John draws a square on a coordinate plane. Then, he draws an image of the square 3 units to the right of the original square. What is true about the corresponding sides on the original figure and the image?

a. The corresponding sides are skew.

b. The corresponding sides intersect at one point.

c. The corresponding sides intersect at an infinite number of points.

d. The corresponding sides are parallel.


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9. Which transformation was used to create ∆ DEF from ∆ ABC ?

x

y

86

46

2

8

2–6

–4–2–8

–8–6

A D

E

FC

B

a. ∆ ABC was reflected over the y -axis.

b. ∆ ABC was translated to the right 3 units and down 1 unit.

c. ∆ ABC was rotated 90° clockwise about the origin.

d. ∆ ABC was translated to the right 1 unit and down 3 units.

10. Which transformation was used to create ∆ GHI from ∆ DEF ?

x

y

86

468

2 4–6 –4

–4

–8

–8–6

GFE

DHI

–2

a. ∆ DEF was rotated 90° counterclockwise about the origin.

b. ∆ DEF was rotated 180° counterclockwise about the origin.

c. ∆ DEF was reflected over the x -axis.

d. ∆ DEF was reflected over the y -axis.


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11. Jon drew a triangle with coordinates (5, 1) , (7, −2) and (3, −1) . He drew an image of the triangle with coordinates (5, −1) , (7, 2) , and (3, 1) . How did he make the image?

a. He translated the original figure 2 units down.

b. He translated the original figure 4 units up.

c. He reflected the original figure over the x -axis.

d. He reflected the original figure over the y -axis.

12. Triangle ABC is transformed to create triangle DEF . What sequence of transformations maps one to the other?

0

2

4

6

8

–2

–4

–6

–8

x

y

–2–4–6–8 2 4 6 8

C

B

A

F

D

E

a. Rotate 180° about the origin, then translate left 2 units

b. Reflect over the x -axis, then translate down 2 units

c. Translate 4 units to the right, then rotate 180° about the origin

d. Translate 2 units to the right, then reflect over the x -axis


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13. Which transformation preserves congruence?

a. rotation

b. reflection

c. translation

d. all of the above

14. Rectangle ABCD is transformed to create rectangle EFGH . What sequence of transformations maps one to the other?

0

2

4

6

8

–2

–4

–6

10

x

y

–2–4–6–8 2 4 6 8

A D

G FB C

H E

a. Reflect over the y -axis, then reflect over the x -axis

b. Rotate 270° counterclockwise about the origin, then translate up 4 units

c. Translate down 4 units, then rotate 180° about the origin

d. Translate 4 units to the right, then rotate 180° about the origin


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15. Which algebraic representation indicates reflecting a shape over the y-axis on the coordinate plane?

a. (x, y) → (x, y – 2)

b. (x, y) → (x – 3, y)

c. (x, y) → (–x, y)

d. (x, y) → (x, –y)

16. A trapezoid is graphed on a coordinate grid and then reflected across the x-axis. Then, the new image of the trapezoid was reflected again, but this time over the y-axis. If a vertex of the original trapezoid is located at (x, y), which ordered pair represents the new vertex after both transformations have been applied?

a. (x, y)

b. (x, –y)

c. (–x, y)

d. (–x, –y)


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SIMILARITY: Standardized Test • 1

SIMILARITY


1. Triangle EFG is dilated with a scale factor of 1 _ 2 to create ∆ E ′F ′G ′ . The measure of ∠F ′ is 36° . What is m∠F ?

a. 18°

b. 36°

c. 72°

d. 144°

2. Given ∆ YES ~ ∆ NOT . Which statement must be true?

a. NO _ YE = OT _ ES = NT _ YS

b. YE _ ES = NO _ NT

c. YE _ NO = ES _ NT = YS _ OT

d. YE = NO, YS = NT, ES = OT

3. Triangle ABC is dilated to produce triangle A′B′C′ with scale factor 3 _ 4 . Which describes the relationship between the two triangles?

a. ∆ A′B′C′ is an enlargement of ∆ ABC .

b. ∆ A′B′C′ is a reduction of ∆ ABC .

c. ∆ A′B′C′≅ ∆ ABC

d. ∆ A′B′C′ is a mirror image of ∆ ABC .

4. A triangle has vertices at ( 1, 1) , ( 1, 2) , and ( 3, 2) . It is dilated by a scale factor of 3 with the origin as the center of dilation to form a similar triangle. What are the coordinates of the vertices of the image?

a. ( 4, 1) , ( 4, 2) , ( 6, 2)

b. ( 1, 4) , ( 1, 5) , ( 3, 5)

c. ( 4, 4) , ( 4, 6) , ( 6, 5)

d. ( 3,3 ) , ( 3, 6) , ( 9, 6)


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SIMILARITY

5. Given ∆ ABC~∆ ADE with AB = 2centimeters, BD = 3centimeters,and DE = 10centimeters.

A

C

ED

B

10 cm

3 cm

2 cm

What is the length of ‾ BC ?

a. 6 2 _ 3 centimeters

b. 5centimeters

c. 4 centimeters

d. 6 centimeters

6. A triangle is dilated with a center of dilation at the origin. Point P is on the figureandP ’isthecorrespondingpointon the image of the dilation. Point P is at (− 2, 3) and P ’isat(− 8, 12) . What is the scale factor?

a. 2

b. 4

c. 6

d. 9


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SIMILARITY

7. Parallelogram ABCD is transformed to create parallelogram A′B′C′D′ . Which shows the sequence of transformations needed to create A′B′C′D′ ?

x–2–4–6–8 2 4 6 80

2

4

6

8

–2

–4

–6

–8

y

A D

B

A’

B’

D’

C’

C

a. a dilation about the origin by a factor of 3 _ 2 and a translation 3 units to the right

b. a dilation about the origin by a factor of 2 _ 3 and a translation 3 units to the right

c. a dilation about the origin by a factor of 3 _ 2 and a translation 3 units to the left

d. a dilation about the origin by a factor of 2 _ 3 and a translation 3 units to the left

8. Which must be true of a scale factor of a dilation if the image is smaller than the originalfigure?

a. The scale factor is negative.

b. The scale factor is between − 1and0.

c. Thescalefactorisbetween0and1.

d. The scale factor is positive.


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SIMILARITY

9. Given ∆ RST is similar to ∆ UVW with RT = 9inches,UW = 5.4inches,and RS = 6inches.

R

S

T

6 in.

9 in. U

V

W5.4 in.

Which is the length of ‾ UV ?

a. 3.6 inches

b. 2.4 inches

c. 8.1 inches

d. 4 inches

10. Triangle FUN, with vertices F (− 2, 4) , U (0, − 5) , and N (− 3, − 8) was dilated to form triangle PET with vertices P (− 1.6, 3.2) , E (0, − 4) , and T (− 2.4, − 6.4) . Which scale factor was used?

a. 1.25

b. − 1

c. 2 _ 3

d. 0.8


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SIMILARITY:StandardizedTest•5

SIMILARITY

11. Trapezoid WXYZ is transformed to create trapezoid W ′X ′Y ′Z ′ . Which shows the sequence of transformations needed to create W ′X ′Y ′Z ′ ?

x–2–4–6–8 64 80

2

4

6

8

–2

–4

–6

–8

y

WZ

W’

X’Y’

Z’

Y X

a. dilation by a factor of 2 about the origin and a translation 1 unit down

b. dilation by a factor of 1 _ 2 about the origin and a translation 1 unit up

c. dilation by a factor of 2 about the origin and a translation 1 unit up

d. dilation by a factor of 1 _ 2 about the origin and a translation 1 unit down

12. Triangle XYZ has been enlarged with P as the center of dilation and scale to form triangle X ′Y ′Z ′.

XX'

Y' Z'

Y Z

P

Which is a correct conclusion?

a. X ′P ____ XP = Y ′P ____ YP = Z ′P ____ ZP

b. ∆ X ′ Y ′ Z ′ ≅ ∆ XYZ

c. X ′ X = XP, Y ′ Y = YP, Z ′ Z = ZP

d. X ′ X = Y ′ Y = Z ′Z


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SIMILARITY

13. Which of the following is true about dilations?

a. Dilated images have the same shape as the original image.

b. Dilated images can be enlargements of the original image.

c. Dilated images can be reductions of the original image.

d. All of the above.

14. Triangle PQR has been reduced with D as the center of dilation and scale to form triangle P′Q′R′ .

D

Q

R

P

P’Q’

R’

Which is the correct conclusion?

a. ∆ PQR is similar to ∆ P′Q′R′

b. ∆ PQR is congruent to ∆ P′Q′R′

c. RD _ R′D = QD _ P′D = PD _ Q′D

d. P′D = Q′D = R′D

15. Which transformation does NOT preserve congruence?

a. (x, y) → (–x, –y)

b. (x, y) → (x–5,y + 2)

c. (x, y) → (–x, y)

d. (x, y) → (2x, 2y)

16. A triangle will be dilated on the coordinate plane to create a larger triangle. The triangle is dilated using the origin as the center of dilation. Which rule could represent this dilation?

a. (x, y) →(0.75–x,0.75–y)

b. (x, y) → (x + 6, y + 6)

c. (x, y) → ( 5 __ 4 x, 5 __ 4 y)

d. (x, y) → ( 1 __ 2 x, 1 __ 2 y)


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SIMILARITY

17. A polygon is graphed on a coordinate plane with (x, y) representing the location of a certain point on the polygon. The polygon is transformed using the rule (x, y) → (ax, ay). Which statement must NOT be true?

a. If a is greater than 1, the image of the polygon is larger than the original polygon.

b. If aisbetween0and1,theimageof the polygon is smaller than the original polygon.

c. If a is greater than 1, the image of the polygon is smaller than the original polygon.

d. If a is equal to 1, the image of the polygon is congruent to the original polygon.

18. Quadrilateral ABCD is dilated with the origin as the center of dilation to create quadrilateral A′B′C′D′.

–4–6–8–9 0

AB

CD

C

B

A D

–4

–6

–8

–2–3

–5

–7

–1

2

4

1

3

–2–3–5–7 –1 2 x

y

1 3

Which rule best represents the dilation that has been applied to quadrilateral ABCD to create quadrilateral A′B′C′D′?

a. (x, y) → ( 1 __ 2 x, 1 __ 2 y)

b. (x, y) → (3x–5,3y–5)

c. (x, y) → (x, 5 __ 2 y)

d. (x, y) → (2x, 2y)


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SIMILARITY

19. Triangle ABC is similar to triangle XYZ.

A

B C

X

YZ

Which proportion must be true?

a. AB ___ XY = BC ___ YZ

b. CA ___ ZY = AB ___ XY

c. AB ___ XZ = BC ___ XY

d. AC ___ XZ = CB ___ YX

20. Pentagon MNPQR is shown on the coordinate plane. Pentagon MNPQR is dilated with the origin as the center of dilation using the rule (x, y) → ( 4 __ 3 x, 4 __ 3 y) to createpentagonM′N′P′Q′R′.

–4–6–8–9–10–11–12 0

–4

–6

–8–9

–10–11–12

–2–3

–5

–7

–1

2

4

6

89

101112

1

3

5

7

–2–3–5–7 –1 2 x

y

P

Q

N

M

R

41 3 6 8 9 10 11 125 7

Which statement is true?

a. Pentagon M′N′P′Q′R′ is larger than pentagon MNPQR, because the scale factor is greater than 1.

b. Pentagon M′N′P′Q′R′ is larger than pentagon MNPQR, because the scale factor is less than 1.

c. Pentagon M′N′P′Q′R′ is smaller than pentagon MNPQR, because the scale factor is greater than 1.

d. Pentagon M′N′P′Q′R′ is smaller than pentagon MNPQR, because the scale factor is less than 1.


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LINE AND ANGLE RELATIONSHIPS: Standardized Test • 1

LINE AND ANGLE RELATIONSHIPS


1. A triangle has angle measures 23° and 35°. Which equation can be used to determine x, the measure of the third angle in the triangle?

a. 23 + 35 = x

b. 90 − 23 − 35 = x

c. x + 58 = 180

d. 90 − x = 58

2. What is the value of x ?

114°

x

76°

a. 38°

b. 57°

c. 76°

d. 85°

3. What is the measure of ∠ACD ?

117°

33°

C DB

A

a. 30°

b. 63°

c. 147°

d. 150°

4. Which theorem states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle?

a. Triangle Sum Theorem

b. Remote Interior Angle Theorem

c. Exterior Angle Theorem

d. Exterior Inequality Theorem


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5. In the figure shown, 𝓁 1 ∥ 𝓁 2 .

1

124°

21

What is m∠1 ?

a. 56°

b. 68°

c. 112°

d. 124°

6. In the figure shown, lines 1 and 2 are parallel.

1 25 6 7 8

3 4

1 2

3

The sum of the measures of angles 4 and 5 is 150°. What is the measure of angle 1?

a. 30°

b. 75°

c. 105°

d. 115°


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7. In the figure shown, lines 1 and 2 are not parallel.

1 2

3 45 6

7 81

3

2

Which lists only angles that are supplements of angle 1?

a. angles 6, 3, and 8

b. angles 2 and 5

c. angles 4 and 8

d. angles 5 and 7

8. In the figure shown, 𝓁 1 ∥ 𝓁 2 and 𝓁 3 ⊥ 𝓁 4 .

57º

2

13

4

x

What is the value of x ?

a. 147°

b. 57°

c. 123°

d. 33°


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9. Which is NOT a correct conclusion about the figure?

P

R

Q

S

T

36°

36°

a. ∆ PQR ∼ ∆ PST by the AA Similarity Theorem.

b. PQ _ QS = PR _ RT = PR _ ST

c. ∠PQR ≅ ∠PST

d. PS _ PQ = PT _ PR = ST _ QR

10. Which is a correct conclusion about the two triangles shown?

Y

ZV

W

X

a. ∆ VWX ∼ ∆ ZYX by the AA Similarity Theorem.

b. ∆ VXW ∼ ∆ XYZ by the AA Similarity Theorem.

c. The triangles are not similar.

d. There is not enough information to determine whether the triangles are similar.


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11. In the figure shown, r ∥ s .

rs

1 2

4 3

5 6

8 7

If m∠2 = 146° and m ∠5 = 2x , what is m∠7 ?

a. 17°

b. 34°

c. 146°

d. 180°


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12. Which is the correct similarity statement?

G

H

J

K

L

60°

60°

a. ∆ GJL ∼ ∆ HJK

b. ∆ GJL ∼ ∆ KJH

c. ∆ JGL ∼ ∆ KJH

d. ∆ LGJ ∼ ∆ HJK

13. In the figure shown, 𝓁 1 ∥ 𝓁 2 .

2

1

12

34

567

8

Which angle is congruent to ∠7 ?

a. ∠5

b. ∠1

c. ∠3

d. All of the above.


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14. When two parallel lines are intersected by a transversal, which pair of angles are always supplementary?

a. corresponding angles

b. vertical angles

c. alternate interior angles

d. same-side exterior angles

15. In the figure shown, a ∥ b .

51 2

6

73 4

8

ab

Which angles are supplements of angle 1?

a. ∠2, ∠4, ∠5, ∠6

b. ∠3, ∠4, ∠6, ∠8

c. ∠2, ∠4, ∠5, ∠7

d. ∠2, ∠3, ∠5, ∠8


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16. Four triangles are shown.

40°

50°

35°

120° 25° 155°

49°

62°w° z°

130° 140° 40°

70°

70°

Based on these triangles, which statement is true?

a. w = 69° , because 49 + 62 = 111 and 180 – 111 = 69

b. w = 111° , because 180 – (49 + 62) = 69 and 180 – 69 = 111

c. w = 291° , because 49 + 62 = 111 and 111 + 180 = 291

d. w = 167° , because 180 – 62 = 118 and 118 + 49 = 167


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17. The measure of angle RST is 46°. The measure of an angle supplementary to angle RST is 2x. What is the value of x?

a. 22º

b. 44º

c. 67º

d. 134º


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18. What is the value of x?

P

M

x

O

N

L

145°

88°

a. 35°

b. 92°

c. 57°

d. 233°


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19. In the figure shown, r ∥ s . If the m∠4 = 132° and m∠6 = 6x , what is the value of x?

r

s6

4

a. 48

b. 8

c. 22

d. 132


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20. Main Street, Broadway Road, and Washington Avenue intersect at one point on the map shown. Main Street and Broadway Road are perpendicular to each other.

The measure of angle 1 is 48º. What is measure of angle 5?

a. 24º

b. 42º

c. 48º

d. 132º


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