geometry winter review 2014-2015 of the new line...

Geometry Winter Review 2014-2015

Student Packet

Name: __________________________________________________ Date:_______________________

MAFS.912.G-CO.4.12

1. Below is a stage in the construction of a line segment congruent to AB with point C as one of the endpoints

of the new line segment.

Which of the following sentences describes the next step in the construction?

A. Set the compass point on point B and adjust the compass width to point C.

B. Mark a point on 𝐴𝐵̅̅ ̅̅ and adjust the compass width to point C from the point.

C. Mark a point on 𝐴𝐵̅̅ ̅̅ and make two arcs on 𝐴𝐵̅̅ ̅̅ centered at the point.

D. Set the compass point on point A and adjust the compass width to point B.

MAFS.912.G-CO.1.2

2. Which of the following transformations does not preserve distance and angle measures?

A. translation

B. reflection

C. rotation

D. horizontal stretch

MAFS.912.G-CO.2.6

3. Is triangle 𝑆𝑇𝑈 congruent to triangle 𝑊𝑋𝑌?

A. Yes. Triangle STU was rotated clockwise 270° about point T, translated 7 units to the right, and translated 6 units

down to create triangle WXY.

B. Yes. Triangle STU was rotated clockwise 270° about point T, translated 4 units to the right, and translated 2 units


C. No. Triangle STU is not congruent to triangle WXY.

D. Yes. Triangle STU was rotated clockwise 90° about point T, translated 7 units to the right, and translated 6 units



Student Packet

MAFS.912.G-CO.4.12

4. Amy made a mistake in creating a copy of ∠𝐴𝐵𝐶. What does she need to correct in the following

construction for copying ∠𝐴𝐵𝐶 with point 𝐸 as the vertex of the new angle?

A. The second arc should be centered at point J and pass through point A.

B. The third arc should be centered at point K and pass through point E.

C. The second arc should be centered at point H and pass through point A.

D. The third arc should be centered at point K and intersect the second arc.

MAFS.912.G-CO.1.3

5. If ∠𝐻 ≅ ∠𝐾, which of the following conditions must also be met to prove that ∆𝐺𝐻𝐽 ≅ ∆𝐿𝐽𝐾 by Angle-

Angle-Side rule?

A. I only

B. I or IV only

C. II only

D. III or IV only


Student Packet

MAFS.912.G-CO.1.3

6. Which transformation carries the regular hexagon EFGHIJ onto itself?

A. a rotation of 60° about its center

B. a rotation of 45° about its center

C. a rotation of 90° about its center

D. a rotation of 30° about its center

MAFS.912.G-CO.3.10

7. Given: ∆𝐴𝐵𝐶 with exterior ∠4

Prove: 𝑚∠4 = 𝑚∠1 + 𝑚∠2

Proof:

Which of the following reasons completes the proof?

A. 𝑚∠4 + 𝑚∠3 = 𝑚∠1 + 𝑚∠2 + 𝑚∠4

B. 𝑚∠1 + 𝑚∠3 + 𝑚∠4 = 180°

C. 𝑚∠1 + 𝑚∠2 + 𝑚∠4 = 180°

D. 𝑚∠4 + 𝑚∠3 = 𝑚∠1 + 𝑚∠2 + 𝑚∠3


Student Packet

MAFS.912.G-CO.2.7

8. Triangles ABC and DEF have two sets of sides of the same length and the included angles between those

sides have the same measure as shown below.

Which of the following point transformations is a result of a sequence of rigid motions that can be used to

show that triangle ABC is congruent to triangle DEF by taking triangle ABC onto triangle DEF?

A. (𝑥, 𝑦) 𝑡𝑜 (−𝑦 + 7, −𝑥)

B. (𝑥, 𝑦) 𝑡𝑜 (−𝑦, −𝑥 + 7)

C. (𝑥, 𝑦) 𝑡𝑜 (−𝑥, −𝑦 + 7)

D. (𝑥, 𝑦) 𝑡𝑜 (−𝑥 + 7, −𝑦)

MAFS.912.G-CO.4.12

9. What is the first step in the construction of an angle bisector using only a compass and straightedge?

A. Mark a point in the angle's interior and draw an arc centered at the point, intersecting both the legs of the

angle.

B. Place the compass needle on one of the legs of the angle and draw an arc intersecting the other leg.

C. Mark a point outside the angle and draw an arc centered at the point, intersecting the vertex of the angle.

D. Place the compass needle on the vertex of the angle and draw an arc across both legs of the angle.

MAFS.912.G-CO.2.7

10. A series of transformations were applied to triangle 𝐽𝐾𝐿 to create triangle 𝑋𝑌𝑍.

If triangle JKL and triangle XYZ are congruent, which of the following transformations could have been

applied to triangle JKL?

A. I and III only

B. I, II, III, and IV

C. I, II, and III only

D. I and II only


Student Packet

MAFS.912.G-CO.3.9

11. Given: 𝑠 ∥ 𝑡 and u is a transversal of s and t.

Prove: ∠1 ≅ ∠5, ∠2 ≅ ∠6, ∠3 ≅ ∠7, 𝑎𝑛𝑑 ∠4 ≅ ∠8

Proof:


A. Two lines cut by a transversal which has a pair of congruent corresponding angles are parallel.

B. Two lines cut by a transversal which has a pair of congruent exterior angles are parallel.

C. Parallel angles postulate.

D. Converse of the parallel angles postulate.

MAFS.912.G-CO.1.2

12. Which of the following transformations will produce a similar, but not congruent figure?

A. dilation

B. reflection

C. rotation

D. translation


Student Packet

MAFS.912.G-CO.3.9

13. Given: ∠2 and ∠3 are a linear pair,

∠3 and ∠4 are a linear pair

Prove: ∠2 ≅ ∠4

Proof:


A. Transitive property

B. Linear pair postulate

C. Congruent complements theorem

D. Right angle congruence theorem

MAFS.912.G-CO.1.3

14. Which transformation carries the regular pentagon below onto itself?

A. a rotation of 36° about the origin

B. a rotation of 45° about the origin

C. a rotation of 115° about the origin

D. a rotation of 72° about the origin


Student Packet

MAFS.912.G-CO.2.8

15. Triangle 𝑀𝑁𝑂 is rotated clockwise 90° to create triangle 𝑈𝑉𝑊.

Is triangle MNO congruent to triangle UVW?

A. Yes, the triangles are congruent by SSS.

B. There is not enough information to determine if the triangles are congruent.

C. No, the triangles are not congruent.

D. Yes, the triangles are congruent by AAA.

MAFS.912.G-CO.1.5

16. What are the coordinates of 𝐻′ if 𝐸′𝐹′𝐺′𝐻′ is a reflection of 𝐸𝐹𝐺𝐻 across the 𝑦 − 𝑎𝑥𝑖𝑠?

A. (-5,-5)

B. (-5,-1)

C. (3,1)

D. (5,1)

MAFS.912.G-CO.3.10

17. If ∆𝑍𝑋𝑌 is an equilateral triangle and 𝑚∠𝑊 = 34°, what is 𝑚∠𝑊𝑋𝑍?

A. 26°

B. 19°

C. 46°

D. 86°


Student Packet

MAFS.912.G-CO.1.5

18. What is the rule for the transformation below?

A. (𝑥′ , 𝑦′) = (−𝑥 − 6 , −𝑦 + 1)

B. (𝑥′ , 𝑦′) = (𝑥 − 6 , −𝑦 + 1)

C. (𝑥′ , 𝑦′) = (𝑥 − 6 , 𝑦 − 1)

D. (𝑥′ , 𝑦′) = (𝑥 − 6 , 𝑦 + 1)

MAFS.912.G-CO.1.5

19. Which of the following sequences of transformations will carry rectangle A onto rectangle B?

A. Rotate rectangle A 90° counterclockwise about the origin, reflect it over the y-axis, and translate it 1 unit up.

B. Translate rectangle A 7 units down, rotate it 180° about the point (2, -6), and translate it 8 units to the left.

C. Reflect rectangle A over the x-axis, translate it 2 units up, and reflect it over the y-axis.

D. Rotate rectangle A 90° clockwise about the origin, and translate it 2 units upand 6 units to the right.


Student Packet

MAFS.912.G-CO.2.8

20. Triangle 𝐽𝐾𝐿 is translated to create triangle 𝑅𝑆𝑇.

Is triangle JKL congruent to triangle RST?

A. Yes, the triangles are congruent by AAA.

B. Yes, the triangles are congruent by SAS.

C. There is not enough information to determine if the triangles are congruent.

D. No, the triangles are not congruent.

MAFS.912.G-CO.3.9

21. In the picture below, two lines intersect at point F. Angle AFC is represented by (9x)° and angle AFB is

represented by (225 - 14x)°.

What is the measure of BFD?

A. 91°

B. 90°

C. 9°

D. 81°

MAFS.912.G-CO.3.9

22. Lines f and g are parallel lines cut by the transversal d. If the measure of ∠2 is 51°, what is the measure of ∠8?

A. 129°

B. 61°

C. 51°

D. 119°

Picture not drawn to scale

Picture not drawn to scale


Student Packet

MAFS.912.G-CO.1.1

23. Which of the following statements is the definition of parallel lines?

A. Two distinct coplanar lines that intersect at a 90°angle.

B. Two distinct coplanar lines that do not intersect.

C. Two rays with a common endpoint that point in opposite directions.

D. Two rays sharing a common endpoint.

MAFS.912.G-GPE.2.6

24. In the reflection of a polygon, which of the following characteristics of the polygon remain the same?

A. I and III

B. I and II

C. I, II, III

D. II and III

MAFS.912.G-GPE.2.7

25. A triangle is shown on the coordinate plane below.

What is the perimeter of the triangle?

A. 10.63 units

B. 25.63 units

C. 28 units

D. 56 units


Student Packet

MAFS.912.G-SRT.1.1

26. Which of the following represents a polygon that is two times the size of the original polygon?

A.

B.

C.

D.

MAFS.912.G-CO.3.10

27. Given isosceles trapezoid ABCD with 𝐷𝐹̅̅ ̅̅ ≅ 𝐶𝐸̅̅ ̅̅ and ∠𝐵𝐴𝐹 ≅ ∠𝐶𝐸𝐵, determine the missing reason to

prove ∆𝐴𝐹𝐷 ≅ ∆𝐶𝐸𝐵.

A. alternate exterior angles conjecture

B. alternate interior angles conjecture

C. vertical angle conjecture

D. corresponding angles conjecture


Student Packet

MAFS.912.G-CO.3.10

28. Given: Point D is the midpoint of 𝐴𝐵̅̅ ̅̅ and point E is the midpoint of segment 𝐴𝐶̅̅ ̅̅ .

Prove: 𝐷𝐸̅̅ ̅̅ ∥ 𝐵𝐶̅̅ ̅̅

Proof:

Which of the following reasons complete the proof?

A. Angle-Angle similarity postulate

B. Triangle Midsegment Theorem

C. Side-Angle-Side similarity theorem

D. Side-Side-Side similarity theorem

MAFS.912.G-SRT.1.1

29. If the scale factor of a dilation is less than one and greater than zero, what happens to the resulting image?

A. The resulting image will be a rotation of the original image.

B. The resulting image will be an enlargement of the original image.

C. The resulting image will be a reduction of the original image.

D. The resulting image will be a translation of the original image.


Student Packet

MAFS.912.G-CO.3.10

30. Complete this proof of the isosceles triangle theorem.

Given: ∆𝐴𝐵𝐶 is isosceles

Construct: ray BD bisecting ∠𝐴𝐵𝐶

Prove: ∠𝐶𝐴𝐵 ≅ ∠𝐵𝐶𝐴

A. SSS congruence

B. SAS congruence

C. AAS congruence

D. SSA congruence

geometry winter review 2014-2015 of the new line...

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