Name____________________________________________ Period____________________

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Review for Geometry Midterm 2015: Chapters 1-5

Short Answer

1. What is the length of AC?

2. Tell whether a triangle can have sides with lengths 1, 2, and 3.

3. Danny and Dana start hiking from the same base camp and head in opposite directions. Danny walks 6 miles due

west, then changes direction and walks for 5 miles to point C. Dana hikes 6 miles due east, then changes direction

and walks for 5 miles to point S. Use the diagram to find which hiker is farther from the base camp.

4. Given: ∆ABC ≅ ∆MNO

Identify all pairs of congruent corresponding parts.

5. 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)

6. What is the slope of the line shown?

Name: ________________________ ID: A

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7. What is the value of x? Identify the missing justifications.

m∠PQR = x − 11, m∠SQR = x + 1, and m∠PQS = 100.

m∠PQR + m∠SQR = m∠PQS a. __________

x – 11 + x + 1 = 100 b. Substitution Property

2x – 10 = 100 c. Simplify

2x = 110 d. __________

x = 55 e. Division Property of Equality

8. Is the line through points P(–8, –1) and Q(–5, 8) parallel to the line through points R(3, 0) and S(1, –4)? Explain.

9. Compare m∠ABC and m∠CBD. 10. Where is the circumcenter of any given triangle?

11. Find the coordinates of the midpoint of the segment

whose endpoints are H(10, 1) and K(8, 3).

Name: ________________________ ID: A

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12. What is the missing reason in the two-column proof?

Given: QS→

bisects ∠TQR and SQ→

bisects ∠TSR

Prove: ∆TQS ≅ ∆RQS

Statements Reasons

1. QS→

bisects ∠TQR 1. Given

2. ∠TQS ≅ ∠RQS 2. Definition of angle bisector

3. QS ≅ QS 3. Reflexive property

4. SQ→

bisects ∠TSR 4. Given

5. ∠TSQ ≅ ∠RSQ 5. Definition of angle bisector

6. ∆TQS ≅ ∆RQS 6. ?

13. What is the value of x?

14. Find the value of x for which l is parallel to m. The

diagram is not to scale.

15. Write an equation in slope-intercept form of the

line through point P(1, 4) with slope –3.

16. Complete the two-column proof.

Given: x

5+ 9 = 11

Prove: x = 10

x

5+ 9 = 11 a. ________

x

5= 2 b. ________

x = 10 c. ________

Name: ________________________ ID: A

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17. Find the value of x. The diagram is not to scale. 18. ∠NPM ≅ ?

19. Tom is wearing his favorite bow tie to the school dance. The bow tie is in the shape of two triangles.

Given: AB ≅ ED , BC ≅ DC , AC ≅ EC , ∠A ≅ ∠E

Prove: ∆ABC ≅ ∆EDC

Complete the proof.

Proof:

Statements Reasons

1. AB ≅ ED , BC ≅ DC , AC ≅ EC 1. Given

2. ∠A ≅ ∠E 2. Given

3. ∠BCA ≅ ∠DCE 3. [1]

4. ∠B ≅ ∠D 4. [2]

5. [3] 5. Definition of congruent triangles

Name: ________________________ ID: A

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20. 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]

21. Determine whether triangles EFG and PQR

are congruent.

22. If Z is the midpoint of RT , what are x, RZ, and RT?

23. Find m∠K .

24. If EF = 8x + 13, FG = 16, and EG = 85, find the

value of x. The drawing is not to scale.

Name: ________________________ ID: A

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25. The diagram shows the approximate distances from

Houston to Dallas and from Austin to Dallas. What

is the range of distances, d, from Austin to

Houston?

26. What are the measures of ∠ABD and ∠ABC?

Classify each angle as acute, right, obtuse, or

straight.

27. Find the value of x. The diagram is not to scale.

Use the diagram to find the following.

28. Identify a pair of alternate exterior angles.

29. Find the value of x. The diagram is not to scale.

30. What additional information do you need to prove

∆ABC ≅ ∆ADC by the SAS Postulate?

Name: ________________________ ID: A

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31. In ∆ACE, G is the centroid and BE = 15. Find BG

and GE.

32. Write the sides of ∆IJK in order from shortest to

longest.

33. Tell whether a triangle can have sides with lengths

5, 11, and 7.

34. MO→

bisects ∠LMN, m∠LMO = 8x − 28, and

m∠NMO = 2x + 38. Solve for x and find m∠LMN.

The diagram is not to scale.

35. The lengths of two sides of a triangle are 3 inches

and 8 inches. Find the range of possible lengths for

the third side, s.

36. Justify the last two steps of the proof.

Given: PQ ≅ SR and PR ≅ SQ

Prove: ∆PQR ≅ ∆SRQ

Proof:

1. PQ ≅ SR 1. Given

2. PR ≅ SQ 2. Given

3. QR ≅ RQ 3. ?

4. ∆PQR ≅ ∆SRQ 4. ?

37. Supplementary angles are two angles whose

measures have a sum of ____.

Complementary angles are two angles whose

measures have a sum of ____.

38. The legs of an isosceles triangle have lengths

3x + 2 and −x + 26. The base has length 2x + 2.

What is the length of the base?

39. For these triangles, select the triangle congruence

statement and the postulate or theorem that

supports it.

Name: ________________________ ID: A

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40. ∆ABC is an isosceles triangle. AB is the longest

side with length 10x + 3. BC = 5x + 5 and CA =

4x + 11. Find AB.

41. Name the line and plane shown in the diagram.

42. What are the names of four coplanar points? 43. Find the value of x.

Name: ________________________ ID: A

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44. Name the angle included by the sides MP and PN . 45. Find the value of k. The diagram is not to scale.

Multiple Choice

Identify the choice that best completes the statement or answers the question.

46. Write an equation in point-slope form & slope- intercept form of the line through point J(10, –2) with slope 7.

a. y + 2 = 7 x + 10( ) c. y − 2 = 7 x + 10( )

b. y + 2 = 7 x − 10( ) d. y + 2 = −7 x − 10( )

47. Which two lines are parallel?

I. 5y = 4x − 5

II. 7y = 5 − 5x

III. 7y + 5x = −1

a. I and III c. II and III

b. I and II d. No, two of the lines are parallel.

48. Where can the bisectors of the angles of an obtuse triangle intersect?

I. inside the triangle

II. on the triangle

III. outside the triangle

a. I only b. III only c. I or III only d. I, II, or II

Name: ________________________ ID: A

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49. Supply the missing reasons to complete the proof.

Given: ∠A ≅ ∠D and AC ≅ DC

Prove: BC ≅ EC

Statement Reasons

1. ∠A ≅ ∠D and

AC ≅ DC

1. Given

2. ∠BCA ≅ ∠ECD 2. Vertical angles are congruent.

3. ∆BCA ≅ ∆ECD 3. ?

4. BC ≅ EC 4. ?

a. ASA; Corresp. parts of ≅ ∆ are ≅. c. AAS; Corresp. parts of ≅ ∆ are ≅.

b. ASA; Substitution d. SAS; Corresp. parts of ≅ ∆ are ≅.

50. Which statement can you conclude is true from the given information?

Given: AB→←

is the perpendicular bisector of IK .

a. A is the midpoint of IK . c. AJ = BJ

b. IJ = JK d. ∠IAJ is a right angle.

ID: A

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Review for Geometry Midterm 2015: Chapters 1-5

Answer Section

SHORT ANSWER

1. 8

2. No

3. Danny is farther from the base camp than Dana.

4. ∠A ≅ ∠M , ∠B ≅ ∠N , ∠C ≅ ∠O, AB ≅ MN , BC ≅ NO, AC ≅ MO

5.

This is a translation 6 units left and 2 units up.

6. 1

7. Angle Addition Postulate; Addition Property of Equality

8. No; the lines have unequal slopes.

9. m∠ABC > m∠CBD

10. the point of concurrency of the bisectors of the angles of the triangle

11. (9, 2)

12. ASA Postulate

13. 68°

14. 95

15. y = –3x + 7

16. a. Given

b. Subtraction Property of Equality

c. Multiplication Property of Equality

17. 11

18. ∠BCA

19. [1] Vertical Angles Theorem

[2] Third Angles Theorem

[3] ∆ABC ≅ ∆EDC

20. [1]. Definition of midpoint

[2] ∠TPR ≅ ∠QPS

[3] SAS

ID: A

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21. The triangles are congruent because EFG can be mapped to PQR by a reflection: (x,y) → (x,−y).

22. x = 14, RZ = 88, and RT = 176

23. m∠K = 63°

24. x = 7

25. 40 < d < 440

26. m∠ABD = 16°; ∠ABD is acute.

m∠ABC = 180°; ∠ABC is straight.

27. 56

28. ∠2 and ∠6

29. 58

30. ∠ACB ≅ ∠ACD

31. BG = 5, GE = 10

32. JK , IK , IJ

33. Yes

34. x = 11, m∠LMN = 120

35. 5 < s < 11

36. Reflexive Property of ≅; SSS

37. 180; 90

38. 14

39. ∆ABC ≅ ∆JKL, HL

40. AB = 63

41. MN→←

and plane M NP

42. Points D, A, B, and J are coplanar.

43. 9

44. ∠P

45. 82

MULTIPLE CHOICE

46. B

47. C

48. A

49. A

50. B