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Analytic Geometry Unit 1 Post-Assessment Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Quadrilaterals A, B, C, and D are shown on the coordinate plane below.

3.

QRS is translated on a coordinate grid. The result of the translation is Q ′R ′S ′. Which statement confirms that QRS is congruent to Q ′R ′S ′? A) A translation makes both triangles right triangles. B) A translation makes both triangles equilateral triangles. C) A translation keeps all of the corresponding sides proportional.

Which quadrilaterals are congruent, and why? D) A translation keeps all of the corresponding pairs of angles and sides congruent.

A) A and C, because they could be rotated and translated to be onto each other.

4. Right

B) A and C, because they could be rotated, translated, and dilated to be onto each other.

JKL is rotated to become right

J ′K ′L ′ .

C) B and D, because they could be rotated and translated to be onto each other. D) B and D, because they could be rotated, translated, and dilated to be onto each other. 2. Which of the following MOST accurately describes a dilation? A) When a shape is dilated, the parallel lines remain parallel.

Which statement could be used to prove JKL ≅ J ′K ′L ′ ?

B) When a shape is dilated, the angles within the shape change.

A) ASA, because JL ≅ J ′L ′ .

C) When a shape is dilated, the orientation of the shape changes.

B) SAS, because JL ≅ J ′L ′ and JK ≅ K ′L ′ . C) SAS, because JK ≅ J ′K ′ and JL ≅ J ′L ′.

D) When a shape is dilated, the distance between points remains the same.

D) ASA. because ∠J ≅ ∠L and JK ≅ K ′L ′ .

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5. In the figure below, b Ä c and line a is a transversal.

7. Sophia is working on the proof below.

What is the appropriate reason for Statement 3 in the proof below?

Which reason explains Statement 2?

A) Opposite angles of a parallelogram are supplementary. A) Vertical Angles Theorem

B) Opposite angles of a parallelogram are congruent.

B) Definition of Congruent Angles C) Linear Pair Postulate

C) Opposite sides of a parallelogram are congruent.

D) Definition of Supplementary Angles

D) Opposite sides of a parallelogram are parallel.

6. In the figure below, NP Ä QR. Find MN.

8. Tara is constructing an equilateral triangle in To which point should she connect point A?

A) x + 8 B) 4x + 2 C) 4x + 6

A) B) C) D)

D) 4x + 8

2

B F E D

X.

For problems 11-13, use

9. Which drawing shows the correct construction of a line segment perpendicular to CD and going through point M?

RST below.

A)

B)

RST undergoes a dilation of 2 with a center of dilation at point S, producing R ′S ′T ′ . 11.

Which of the following statements is true?

C) A) RS Ä R ′S ′ B) RT Ä R ′T ′ D)

C) ST Ä S ′T ′ D) SR Ä S ′T ′ 12. What is the length of R ′T ′ ?

10. A) 5 B) 10 C) 13 D) 2 13 In ABD above, if AB Ä CE , which of these statements could be proven? 13. Which of the following proportions is true? A)

B)

C)

D)

AB BC = CE CD

A)

ST 1 = S ′T ′ 2

B)

2 ST = S ′T ′ 1

AE ED = BC CD

C)

3 RT = R ′T ′ 2

ED AE = EC AB

D)

2 RT = R ′T ′ 3

AB DE = AD CE

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14.

Use the chart below for problems 16 and 17.

JAG is located in the first quadrant of a coordinate grid. The triangle undergoes a transformation so that the resulting triangle remains in the first quadrant. Some measurements of the triangles are shown in the table below. Which of the three triangles shown below is similar to ABC ?

Before After

JA 27 18

∠A

∠G

0

37 0 37 0

72 72 0

16. Which transformation occurred? A) dilation A) I, II, and III

B) rotation

B) I and II only

C) reflection

C) I and III only

D) translation

D) II and III only 17. What of the following statements is true about both triangles?

15. Emilio had a map of Seaside Zoo. He noticed that when he connected the points for the places he wanted to go, it created two similar triangles.

A) They are right triangles. B) They are similar triangles. C) They are isosceles triangles. D) They are congruent triangles. 18. If CAT ≅ to TC ?

Using the given diagram, which of the following explains why ACE ∼ BCD ?

A) OG

A) Angle-Angle Similarity Postulate

B) OD

B) Transitive Property

C) GO

C) Side-Side-Side Similarity Postulate

D) GD

D) Side-Angle-Side Similarity Postulate

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DOG, which side would correspond

19. Which of the following reasons is correct for statement 5?

A) SSS B) SAS C) ASA D) AAA

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Short Answer 20.

Choose one of the reasons below for each statement in the proof . A. Given B. If three or more adjacent angles form a straight angle, their sum is 180 0 . C. If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. D. Substitution property of equality E. If angles are congruent, then they have equal measures. F. Through a point not on a line there is exactly one line parallel to the given line.

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ID: A

Analytic Geometry Unit 1 Post-Assessment Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS:

C A D C A D C C C C B D A A A A B D B

PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS:

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

STA: STA: STA: STA: STA: STA: STA: STA: STA: STA: STA: STA: STA: STA: STA: STA: STA: STA: STA:

G.CO.6 G.SRT.1a G.CO.7 G.CO.8 G.CO.9 G.SRT.5 G.CO.11 G.CO.13 G.CO.12 G.SRT.4 G.SRT.1a G.SRT.1b G.SRT.1b G.SRT.2 G.SRT.5 G.SRT.3 G.SRT.3 G.CO.7 G.CO.10

SHORT ANSWER 20. ANS: 1. A) Given 2. F) Through a point not on a line there is exactly one line parallel to the given line. 3. C) If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. 4. E) If angles are congruent, then they have equal measures. 5. B) If three or more adjacent angles form a straight angle, their sum is 180° 6. D) Substitution property of equality. PTS: 1

STA: G.CO.10

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