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
1
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
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