Foundations of Math 2: Review for Benchmark #3 Foundations ...mrsbealemath.weebly.com/uploads/8/7/5/0/87504342/foundations_o… · Foundations of Math 2 page 2 Foundations of Math

Foundations of Math 2: Review for Benchmark #3 Foundations of Math 2

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1. Which of the following is not a proper way toname the angle shown below?

A. ∠ACB B. ∠CBA

C. ∠B D. ∠3

2. Angle XYZ is shown.

Which point lies in the interior of angle XYZ?

A. point V B. point W

C. point X D. point Y

3. Look at the drawing below.

Note: The figure is not drawn to scale.

What is the measure of angle A?

A. 20◦ B. 45◦ C. 55◦ D. 70◦

4. The diagram below shows angles formed byintersecting lines.

Which answer reflects the relationship between ∠2and ∠3?

A. ∠2 and ∠3 are vertical angles.

B. ∠2 and ∠3 are corresponding angles.

C. ∠2 and ∠3 are alternate exterior angles.

D. ∠2 and ∠3 are adjacent supplementaryangles.

5. What is the supplement of a 40◦ angle?

A. 50◦ B. 130◦ C. 140◦ D. 220◦

6. Use the diagram below to answer the question.

What is the measure of x?

A. 26◦ B. 64◦ C. 90◦ D. 116◦

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7. Angle J and angle K are vertical angles, as shownin the figure below.

The measure of angle J is 46◦.

What is the measure of angle K?

A. 44◦ B. 46◦ C. 134◦ D. 136◦

8. In the figure below,−−→BD intersects

←→AC at point B.

What is the measure of ∠ABD?

A. 68◦ B. 112◦ C. 124◦ D. 170◦

9. In the accompanying diagram, line a intersectsline b.

What is the value of x?

A. −10 B. 5 C. 10 D. 90

10. Choose the correct solution for the equation:5x + 8 = 43

A. x = 10 B. x = 7

C. x = 175 D. x = 5

11. What is the solution to the equation below?

3(x − 4) = 5x − 6

A. x = −3 B. x = 34

C. x = 1 D. x = 9

12. What value of x makes the equation below true?

x9

+ 6 = 8

A. 2 B. 18 C. 66 D. 126

13. If the coordinates of A are (3, 4) and thecoordinates of B are (−3,−4), then the length of−−−AB is

A. 5 B. 10 C. 20 D. 100

14.

What is the value of x in the triangle shownabove?

A. 11 B. 13 C. 17 D. 169

15. What is the midpoint of the line segmentconnecting the points (−2, 4) and (5,−2)?

A.(

32 , 1

)B.

(3, 3

2

)C.

(72 , 1

)D.

(32 , 2

)Foundations of Math 2 page 2 Foundations of Math 2: Review for Benchmark #3

16. In the graph below, figure M was rotated clockwiseabout the origin to generate figure T .

What was the angle of rotation of figure M aboutthe origin?

A. 90◦ B. 180◦ C. 270◦ D. 360◦

17. Renee drew triangle A on a coordinate grid. Thenshe used one transformation of triangle A to createtriangle B, as shown below.

Which transformation did Renee use to createtriangle B ?

A. Dilation B. Rotation

C. Reflection D. Translation

18. Study ^RST on the grid below.

When ^RST is translated 4 units down, what arethe apparent coordinate of T ′ ?

A. (−8,−1) B. (−4,−1)

C. (−1,−8) D. (0,−4)

19. If triangle ABC is rotated 180 degrees about theorigin, what are the coordinates of A′?

A. (−5,−4) B. (−5, 4)

C. (−4, 5) D. (−4,−5)

Foundations of Math 2 page 3 Foundations of Math 2: Review for Benchmark #3

20. Use the figure below to answer the question thatfollows.

A graphic artist needs to reflect triangle ABCacross the x-axis to create Figure A’B’C’. Whatare the coordinates of A’?

A. (1,−2) B. (2,−1)

C. (−1, 2) D. (−2, 1)

21. If quadrilateral QRST is reflected across the y-axis,what will be the coordinates of point Q′?

A. (−2, 4) B. (−2, 1)

C. (−1, 2) D. (−1, 4)

22. Look at ^PQR on this grid.

What are the coordinates of the image of point Rafter a 90◦ counterclockwise rotation about theorigin?

A. (−6,−2) B. (−2,−6)

C. (6,−2) D. (6, 2)

23. In the coordinate plane, right triangle XYZ isreflected over the line y = x.

What are the coordinates of the vertex of the rightangle in ^X′Y ′Z′?

A. (3, 1) B. (3, 0)

C. (1,−3) D. (1,−2)


24. The vertices of ÂBC are A(2, 1), B(3, 4), andC(1, 3). If ÂBC is translated 1 unit down and3 units to the left to create ^DEF, what are thecoordinates of the vertices of ^DEF?

A. D(0, 1), E(1, 2), F(1, 3)

B. D(0,−1), E(0, 3), F(−2,−2)

C. D(−2, 2), E(0, 3), F(−1, 0)

D. D(−1, 0), E(0, 3), F(−2, 2)

25. What are the coordinates of the image of pointP(1, 4) after a clockwise rotation of 90◦ about theorigin?

A. (4,−1) B. (4, 1)

C. (1,−4) D. (−1,−4)

26. What value of x would make the equation2

3=

8

xtrue?

A. 3 B. 9 C. 12 D. 24

27. A right triangle is shown below.

What is the value, in degrees, of x?

A. 25 B. 35 C. 45 D. 55

28. In the figure below, ÂBC is a right triangle andm∠A = 40◦.

What is m∠ECD?

A. 40◦ B. 50◦ C. 130◦ D. 140◦

29. What is m∠x?

A. 35◦ B. 60◦ C. 85◦ D. 95◦


30. The diagram below shows three intersecting lines.

Based on the measurements in the diagram, whatis x ?

A. 65◦ B. 80◦ C. 100◦ D. 115◦

31. Triangle ABC is shown below.

What is the cosine of angle B?

A. 35 B. 4

5 C. 54 D. 5

3

32. Use the triangle to answer the question.

Triangle PQR is a scalene right triangle. Whichof the following is correct?

A. cosP =rp

B. sinQ =qp

C. cosP =pr

D. tanQ =qp

33. In the accompanying diagram, m∠A = 32◦ andAC = 10. Which equation could be used to find xin ÂBC?

A. x = 10 sin 32◦ B. x = 10 cos 32◦

C. x = 10 tan 32◦ D. x =10

cos 32◦


34. A ladder leaning against a house is shown below.


What is the distance (x) from the base of theladder to the house? Round the answer to thenearest foot.

A. 13 feet B. 17 feet

C. 21 feet D. 36 feet

35. A lighthouse, which is 18 feet high, stands on acliff that is 150 feet above sea level. The distancefrom the top of the lighthouse to a sailboat on theocean is 360 feet.


What is the angle of elevation (x) from thesailboat to the top of the lighthouse? Round theanswer to the nearest degree.

A. 25◦ B. 28◦ C. 62◦ D. 65◦

36. Right triangle JKL is shown below.


What is the measure of ∠J? Round the answer tothe nearest degree.

A. 34◦ B. 42◦ C. 48◦ D. 56◦

37. In the accompanying diagram of right triangleABC, a right angle is at C, AB = 26, andm∠A = 27. Find the length of

−−−BC to the nearest

tenth.

38. In right triangle ABC shown below, AB = 18.3 andBC = 11.2.

What is the measure of ∠A, to the nearest tenthof a degree?

A. 31.5 B. 37.7 C. 52.3 D. 58.5


39. In the diagram below, ÂEC ∼= ^BED.

Which statement is not always true?

A.−−−AC ∼=

−−−BD B.

−−−CE ∼=

−−−DE

C. ∠EAC ∼= ∠EBD D. ∠ACE ∼= ∠DBE

40. Triangle ABC is shown in the diagram below.

If−−−DE joins the midpoints of

−−−−−ADC and

−−−−−AEB, which

statement is not true?

A. DE =1

2CB B.

−−−DE ‖

−−−CB

C.ADDC

=DECB

D. ÂBC ∼ ÂED

41. In the accompanying diagram, ^QRS is similar to^LMN, RQ = 30, QS = 21, SR = 27, and LN = 7.What is the length of

−−−ML?

42. In the accompanying diagram, ÂBC is similarto ^DEF with ∠A ∼= ∠D and ∠B ∼= ∠E. IfAC = 4.5, AB = 4, DF = x, and DE = 5, find thevalue of x.

43. If triangles EFG and JKL are congruent, thenwhich two segments must be congruent?

A.−−−EF and

−−−JK B.

−−−EF and

−−JL

C.−−−FG and

−−−JK D.

−−−FG and

−−JL


44. Triangles GHJ and KLM are congruent. Thetriangles and some of their angle measures areshown in the diagram below.

Based on the angle measures in the diagram, whatis m∠JGH?

A. 30◦ B. 35◦ C. 40◦ D. 45◦

45. In the diagram below, triangle FHG is congruentto triangle XZY .

What is the measure of angle X ?

A. 23◦ B. 32◦ C. 55◦ D. 93◦

46. Which theorem can be used to prove that thetriangles in the figure below are congruent?

A. side-by-side (SSS)

B. side-angle-side (SAS)

C. angle-side-angle (ASA)

D. angle-angle-side (AAS)

47. Which theorem of congruence should be used toprove ^QRS ∼= ^TUV?

A. Angle-Side-Angle (ASA)

B. Angle-Angle-Side (AAS)

C. Side-Angle-Side (SAS)

D. Side-Side-Side (SSS)


48. In the diagram below,−−−RT intersects

−−−−QU at point S.

Which postulate should be used to prove that^RQS ∼= ^TUS?

A. Side–Side–Side B. Angle–Side–Angle

C. Angle–Side–Side D. Side–Angle–Side

49. Given:−−−AB and

−−−CD intersect at point E;

∠1 ∼= ∠2

Which theorem or postulate can be used to proveÂED ∼ ^BEC?

A. AA B. SSS C. ASA D. SAS

50. Can we prove ^LMN is congruent to ^XYZ? Isso, which postulate can we use to do so?

A. Yes, we can prove they are congruent usingthe SAS postulate.

B. Yes, we can prove they are congruent usingthe ASA postulate.

C. No, we cannot prove they are congruentbecause ^XYZ appears to be a right triangleand ^LMN is not a right triangle.

D. No, we cannot prove they are congruentbecause none of the three postulates can beused.


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Foundations of Math 2 Foundations of Math 2: Review for Benchmark #3 11/30/2016

1.Answer: A

2.Answer: B

3.Answer: D

4.Answer: D

5.Answer: C

6.Answer: B

7.Answer: B

8.Answer: B

9.Answer: C

10.Answer: B

11.Answer: A

12.Answer: B

13.Answer: B

14.Answer: B

15.Answer: A

16.Answer: B

17.Answer: D

18.Answer: C

19.Answer: A

20.Answer: A

21.Answer: C

22.Answer: B

23.Answer: A

24.Answer: D

25.Answer: A

26.Answer: C

27.Answer: B

28.Answer: B

29.Answer: C

30.Answer: A

31.Answer: A

32.Answer: D

33.Answer: C

34.Answer:

35.Answer:

36.Answer:

37.Answer: 11.8

38.Answer: A

39.Answer: D

40.Answer: C

Teacher’s Key Page 2

41.Answer: 10, and appropriate work is shown.

42.Answer: 7.5

43.Answer: A

44.Answer: A

45.Answer: B

46.Answer: B

47.Answer: B

48.Answer: B

49.Answer: A

50.Answer: D

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