Name: ________________________ Class: ___________________ Date: __________ ID: A

1

GA Milestone Review Unit 1

____ 1. The map shows a linear section of Highway 35. Today, the Ybarras plan to drive the 360 miles from

Springfield to Junction City. They will stop for lunch in Roseburg, which is at the midpoint of the trip. If they

have already traveled 55 miles this morning, how much farther must they travel before they stop for lunch?

a. 125 mi c. 180 mi

b. 145 mi d. 305 mi

____ 2. K is the midpoint of JL. JK = 6x and KL = 3x + 3. Find JK, KL, and JL.

a. JK = 1, KL = 1, JL = 2 c. JK = 12, KL = 12, JL = 6

b. JK = 6, KL = 6, JL = 12 d. JK = 18, KL = 18, JL = 36

____ 3. BD→

bisects ∠ABC, m∠ABD = (7x − 1)°, and m∠DBC = (4x + 8)°. Find m∠ABD.

a. m∠ABD = 22° c. m∠ABD = 40°

b. m∠ABD = 3° d. m∠ABD = 20°

____ 4. Two angles with measures (2x2+ 3x − 5)° and (x2

+ 11x − 7)° are supplementary. Find the value of x and the

measure of each angle.

a. x = 5; 60°; 30° c. x = 5; 60°; 120°

b. x = 6; 85°; 95° d. x = 4; 40°; 90°

____ 5. Two lines intersect to form two pairs of vertical angles. ∠1 with measure (20x + 7)° and ∠3 with measure

(5x + 7y + 49)° are vertical angles. ∠2 with measure (3x − 2y + 30)° and ∠4 are vertical angles. Find the

values x and y and the measures of all four angles.

a. x = 6; y = 10; 127°; 127°; 28°; 28° c. x = 5; y = 5; 107°; 107°; 73°; 73°

b. x = 8; y = 11, 167°; 167°; 13°; 13° d. x = 7; y = 9; 147°; 147°; 33°; 33°

Name: ________________________ ID: A

2

____ 6. Write a justification for each step, given that EG = FH .

EG = FH Given informationEG = EF + FG [1]FH = FG + GH Segment Addition PostulateEF + FG = FG + GH [2]EF = GH Subtraction Property of Equality

a. [1] Angle Addition Postulate

[2] Subtraction Property of Equality

b. [1] Substitution Property of Equality

[2] Transitive Property of Equality

c. [1] Segment Addition Postulate

[2] Definition of congruent segments

d. [1] Segment Addition Postulate

[2] Substitution Property of Equality

____ 7. Find m∠ABC.

a. m∠ABC = 40° c. m∠ABC = 35°

b. m∠ABC = 45° d. m∠ABC = 50°

Name: ________________________ ID: A

3

____ 8. Write and solve an inequality for x.

a. x > 2 c. x > 1

b. x < 2 d. x < −2

____ 9. Write a justification for each step.

m∠JKL = 100°

m∠JKL = m∠JKM + m∠MKL [1]100° = (6x + 8)° + (2x − 4)° Substitution Property of Equality

100 = 8x + 4 Simplify.96 = 8x Subtraction Property of Equality12 = x [2]x = 12 Symmetric Property of Equality

a. [1] Transitive Property of Equality

[2] Division Property of Equality

b. [1] Angle Addition Postulate

[2] Division Property of Equality

c. [1] Angle Addition Postulate

[2] Simplify.

d. [1] Segment Addition Postulate

[2] Multiplication Property of Equality

Name: ________________________ ID: A

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____ 10. A gardener has 26 feet of fencing for a garden. To find the width of the rectangular garden, the gardener uses

the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width of the rectangle. The

gardener wants to fence a garden that is 8 feet long. How wide is the garden? Solve the equation for w, and

justify each step.

P = 2l + 2w Given equation26 = 2(8) + 2w [1]

26 = 16 + 2w

−16 = −16

10 = 2w

Simplify.

Subtraction Property of Equality

Simplify.

102

=2w

2[2]

5 = w Simplify.w = 5 Symmetric Property of Equality

a. [1] Substitution Property of Equality

[2] Division Property of Equality

The garden is 5 ft wide.

c. [1] Substitution Property of Equality

[2] Subtraction Property of Equality

The garden is 5 ft wide.

b. [1] Simplify

[2] Division Property of Equality

The garden is 5 ft wide.

d. [1] Subtraction Property of Equality

[2] Simplify

The garden is 5 ft wide.

____ 11. Find m∠RST .

a. m∠RST = 108° c. m∠RST = 156°

b. m∠RST = 24° d. m∠RST = 72°

____ 12. Three vertices of parallelogram WXYZ are X(–2,–3), Y(0, 5), and Z(7, 7). Find the coordinates of vertex W.

a. (4, 0) c. (5, 0)

b. (9, 15) d. (5, –1)

Name: ________________________ ID: A

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____ 13. Fill in the blanks to complete the two-column proof.

Given: ∠1 and ∠2 are supplementary. m∠1 = 135°

Prove: m∠2 = 45°

Proof:

Statements Reasons

1. ∠1 and ∠2 are supplementary. 1. Given

2. [1] 2. Given

3. m∠1 + m∠2 = 180° 3. [2]

4. 135° + m∠2 = 180° 4. Substitution Property

5. m∠2 = 45° 5. [3]

a. [1] m∠2 = 135°

[2] Definition of supplementary angles

[3] Subtraction Property of Equality

b. [1] m∠1 = 135°

[2] Definition of supplementary angles

[3] Substitution Property

c. [1] m∠1 = 135°

[2] Definition of supplementary angles

[3] Subtraction Property of Equality

d. [1] m∠1 = 135°

[2] Definition of complementary angles

[3] Subtraction Property of Equality

____ 14. A video game designer is modeling a tower that is 320 ft high and 260 ft wide. She creates a model so that

the similarity ratio of the model to the tower is 1

500. What is the height and the width of the model in inches?

a. height = 0.64 in.; width = 0.52 in.

b. height = 3840 in.; width = 3120 in.

c. height = 7.68 in.; width = 6.24 in.

d. height = 160,000 in.; width = 130,000 in.

Name: ________________________ ID: A

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____ 15. Use the given flowchart proof to write a two-column proof of the statement AF ≅ FD.

Flowchart proof:

AB = CD;BF = FC

AB + BF = AF

FC + CD = FD

Given

Segment

Addition

Postulate

AB + BF =

FC + CDAF = FD AF ≅ FD

Addition

Property of

Equality

Substitution Definition of

congruent segments

Complete the proof.

Two-column proof:

Statements Reasons

1. AB = CD; BF = FC 1. Given

2. [1] 2. Addition Property of Equality

3. [2] 3. Segment Addition Postulate

4. AF = FD 4. Substitution

5. AF ≅ FD 5. Definition of congruent segments

a. [1] AB + BF = AF ; FC + CD = FD

[2] AF = FD

b. [1] AF = FD

[2] AB + BF = FC + CD

c. [1] AB = CD; BF = FC

[2] AB + BF = FC + CD

d. [1] AB + BF = FC + CD

[2] AB + BF = AF ;FC + CD = FD

Name: ________________________ ID: A

7

____ 16. Use the given two-column proof to write a flowchart proof.

Given: ∠1 ≅ ∠4

Prove: m∠2 = m∠3

Two-column proof:

Statements Reasons

1. ∠1 ≅ ∠4 1. Given

2. ∠1 and ∠2 are supplementary. ∠3 and ∠4

are supplementary.

2. Definition of linear pair

3. ∠2 ≅ ∠3 3. Congruent Supplements Theorem

4. m∠2 = m∠3 4. Definition of congruent segments

Complete the proof.

Flowchart proof:

∠1 ≅ ∠4

Given

[1] ∠2 ≅ ∠3 m∠2 = m∠3

Definition of linear pair [2] Definition of

congruent segments

a. [1] ∠1 and ∠2 are supplements; ∠3 and ∠4 are supplementary

[2] Congruent Complements Theorem

b. [1] ∠1 and ∠2 are supplementary; ∠3 and ∠4 are supplementary

[2] Congruent Supplements Theorem

c. [1] ∠2 ≅ ∠3

[2] Definition of congruent segments

d. [1] Definition of congruent segments

[2] Congruent Supplements Theorem

Name: ________________________ ID: A

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____ 17. Use the given paragraph proof to write a two-column proof.

Given: ∠BAC is a right angle. ∠1 ≅ ∠3

Prove: ∠2 and ∠3 are complementary.

Paragraph proof:

Since ∠BAC is a right angle, m∠BAC = 90° by the definition of a right angle. By the Angle Addition

Postulate, m∠BAC = m∠1 + m∠2. By substitution, m∠1 + m∠2 = 90°. Since ∠1 ≅ ∠3, m∠1 = m∠3 by the

definition of congruent angles. Using substitution, m∠3 + m∠2 = 90°. Thus, by the definition of

complementary angles, ∠2 and ∠3 are complementary.

Complete the proof.

Two-column proof:

Statements Reasons

1. ∠BAC is a right angle. ∠1 ≅ ∠3 1. Given

2. m∠BAC = 90° 2. Definition of a right angle

3. m∠BAC = m∠1 + m∠2 3. [1]

4. m∠1 + m∠2 = 90° 4. Substitution

5. m∠1 = m∠3 5. [2]

6. m∠3 + m∠2 = 90° 6. Substitution

7. ∠2 and ∠3 are complementary. 7. Definition of complementary angles

a. [1] Substitution

[2] Definition of congruent angles

c. [1] Angle Addition Postulate

[2] Definition of equality

b. [1] Angle Addition Postulate

[2] Definition of congruent angles

d. [1] Substitution

[2] Definition of equality

Name: ________________________ ID: A

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____ 18. Find the value of x.

a. x = 6 c. x = 2

b. x = 4 d. x = 8

____ 19. Determine whether triangles EFG and PQR are congruent.

a. The triangles are congruent because EFG can be mapped to PQR by a reflection:

(x, y) → (−x, y).

b. The triangles are congruent because EFG can be mapped to PQR by a rotation:

(x, y) → (−y, −x).

c. The triangles are congruent because EFG can be mapped to PQR by a reflection:

(x, y) → (x, −y).

d. The triangles are congruent because EFG can be mapped to PQR by a rotation:

(x, y) → (−y, x).

Name: ________________________ ID: A

10

____ 20. Given that ∆ABC ≅ ∆DEC and m∠E = 23°, find m∠ACB.

a. m∠ACB = 77° c. m∠ACB = 23°

b. m∠ACB = 67° d. m∠ACB = 113°

____ 21. Find m∠K .

a. m∠K = 63° c. m∠K = 79°

b. m∠K = 55° d. m∠K = 39°

Name: ________________________ ID: A

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____ 22. Apply the transformation M to the triangle with the given vertices.

Identify and describe the transformation.

M: (x, y) → (x – 6, y + 2)

E(3, 0), F(1, –2), G(5, –4)

a.

This is a translation 6 units left and 2

units up.

c.

This is a translation 6 units left.

b.

This is a translation 2 units left and 6

units up.

d.

This is a translation 6 units left and 2

units down.

Name: ________________________ ID: A

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____ 23. Apply the transformation M to the polygon with the given vertices.

Identify and describe the transformation.

M: (x, y) → (–x, –y)

A(–3, 6), B(–3, 1), C(1, 1), D(1, 6)

a.

This is a rotation of 180° about the

origin.

c.

This is a reflection over the x-axis.

b.

This is a rotation of 180° about the

origin.

d.

This is a rotation of 90° clockwise about

the origin.

Name: ________________________ ID: A

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____ 24. Find m∠E and m∠N , given m∠F = m∠P, m∠E = (x2)°, and m∠N = (4x2− 75)°.

a. m∠E = 25°, m∠N = 25° c. m∠E = 65°, m∠N = 25°

b. m∠E = 25°, m∠N = 65° d. m∠E = 65°, m∠N = 65°

____ 25. Given: P is the midpoint of TQ and RS .

Prove: ∆TPR ≅ ∆QPS

Complete the proof.

Proof:

Statements Reasons

1. P is the midpoint of TQ and RS . 1. Given

2. TP ≅ QP, RP ≅ SP 2. [1]

3. [2] 3. Vertical Angles Theorem

4. ∆TPR ≅ ∆QPS 4. [3]

a. [1]. Definition of midpoint

[2] ∠TPR ≅ ∠QPS

[3] SAS

c. [1] Definition of midpoint

[2] ∠PRT ≅ ∠PSQ

[3] SAS

b. [1] Definition of midpoint

[2] RT ≅ SQ

[3] SSS

d. [1] Definition of midpoint

[2] ∠TPR ≅ ∠QPS

[3] SSS

Name: ________________________ ID: A

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____ 26. What additional information do you need to prove ∆ABC ≅ ∆ADC by the SAS Postulate?

a. AB ≅ AD c. ∠ABC ≅ ∠ADC

b. ∠ACB ≅ ∠ACD d. BC ≅ DC

____ 27. Determine if you can use ASA to prove ∆CBA ≅ ∆CED. Explain.

a. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. No other congruence

relationships can be determined, so ASA cannot be applied.

b. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Adjacent

Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.

c. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles

Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.

d. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles

Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by SAS.

Name: ________________________ ID: A

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____ 28. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.

a. ∆ABC ≅ ∆JLK , HL c. ∆ABC ≅ ∆JLK , SAS

b. ∆ABC ≅ ∆JKL, HL d. ∆ABC ≅ ∆JKL, SAS

____ 29. Two Seyfert galaxies, BW Tauri and M77, represented by points A and B, are equidistant from Earth,

represented by point C. What is m∠A?

a. m∠A = 65° c. m∠A = 50°

b. m∠A = 115° d. m∠A = 60°

Name: ________________________ ID: A

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____ 30. Given ∆ABC with AB = 3, BC = 5, and CA = 6, find the length of midsegment XY .

a. XY = 3 c. XY = 2.5

b. XY = 1.5 d. XY = 2

____ 31. Point O is the centroid of ∆ABC, BY = 3.3 and CO = 3. Find BO.

a. BO = 2.2 c. BO = 3.3

b. BO = 1.1 d. BO = 3

____ 32. Given that YW→

bisects ∠XYZ and WZ = 4.23, find WX .

a. WX = 4.23 c. WX = 45°

b. WX = 8.46 d. WX = 90°

Name: ________________________ ID: A

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____ 33. The diagram shows a new kind of triangular bread. Where should the baker place her hand while spinning the

dough so that the triangle is balanced?

a. 1, 1ÊËÁÁ ˆ

¯˜̃ c.

1

2, 1

Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜

b. 1, 0ÊËÁÁ ˆ

¯˜̃ d.

3

2, 1

Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜

____ 34. The diagram shows the parallelogram-shaped component that attaches a car’s rearview mirror to the car. In

parallelogram RSTU, UR = 25, RX = 16, and m∠STU = 42.4o. Find ST, XT, and m∠RST.

a. ST = 16, m∠RST = 42.4°, XT = 25 c. ST = 25, m∠RST = 137.6°, XT = 16

b. ST = 25, m∠RST = 47.8°, XT = 16 d. ST = 5, m∠RST = 137.6°, XT = 4

____ 35. MNOP is a parallelogram. Find MP.

a. MP = 25 c. MP = 20

b. MP = 30 d. MP = 6

Name: ________________________ ID: A

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____ 36. An artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center

of the quilt. The dimensions of the rectangle are AB = 10 inches and AC = 14 inches. Find BX .

a. BX = 7 inches c. BX = 5 inches

b. BX = 10 inches d. BX = 14 inches

____ 37. TRSU is a rhombus. Find SU .

a. SU = 7 c. SU = 5

b. SU = 1 d. SU = 3

____ 38. Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points.D: (x, y) → (3x, 3y)

J(1, 4), K(6, 4), L(6, 1), M(1, 1)

a. J´(12, 3), K´(12, 18),

L´(3, 18), M´(3, 3)

c. J´(3, 12), K´(18, 12),

L´(18, 3), M´(3, 3)

b. J´(–3, –12), K´(–18, –12),

L´(–18, –3), M´(–3, –3)

d. J´(3, 12), K´(18, 12),

L´(6, 1), M´(1, 1)

Name: ________________________ ID: A

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____ 39. To find out how wide a river is, Jon and Sally mark an X at the spot directly across from a big rock on the

other side of the river. Then they walk in a straight line along the river, perpendicular to the straight line

between the X and the rock. After walking for 20 feet Jon stops while Sally continues along the straight line

for another 10 feet. Then she makes a 90 degree turn and walks for 30 feet. When she stops and looks at the

rock she sees that the straight line from her to the rock passes through Jon. What is the distance from X to the

rock?

a. 30 feet c. 60 feet

b. 50 feet d. 63 feet

____ 40. Find NP.

a. NP = 1 c. NP = 1.6

b. NP = 1.25 d. NP = 2

Name: ________________________ ID: A

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____ 41. An artist used perspective to draw guidelines in her picture of a row of parallel buildings. How many

centimeters is it from Point B to Point C?

a. 1 cm c. 4 cm

b. 3.75 cm d. 2.4 cm

____ 42. Find BD.

a. BD = 5 c. BD = 10

b. BD = 22 d. BD = 12

Name: ________________________ ID: A

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____ 43. Given that ∆KON ∼ ∆LOM, find the coordinates of L and the scale factor.

a. L (6, 0) and scale factor is 2 c. L (9, 0) and scale factor is 4

3

b. L (9, 0) and scale factor is 3 d. L (6, 0) and scale factor is 3

____ 44. Find m∠1 in the diagram. (Hint: Draw a line parallel to the given parallel lines.)

a. m∠1 = 95° c. m∠1 = 85°

b. m∠1 = 80° d. m∠1 = 75°

45. Find the value of x in the rhombus.

Name: ________________________ ID: A

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46. Find the value of x so that m Ä n.

47. Find the value of n in the triangle.

ID: A

1

GA Milestone Review Unit 1

Answer Section

1. A

2. B

3. D

4. B

5. D

6. D

7. C

8. A

9. B

10. A

11. D

12. D

13. C

14. C

15. D

16. B

17. B

18. A

19. C

20. B

21. A

22. A

23. B

24. A

25. A

26. B

27. C

28. B

29. A

30. B

31. A

32. A

33. A

34. C

35. B

36. A

37. A

38. C

39. C

40. B

41. B

42. D

ID: A

2

43. B

44. C

45. 0.5

46. 17

47. 11