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Name: ________________________ Class: ___________________ Date: __________
ID: A
Honors Geometry Sem.1 Exam Review, 12-13
Your Honors Geometry Semester 1 Exam will have 2 parts: a multiple choice section and a free-response section.
The free-response section will consist of approx. 1 question from each chapter test we’ve had thus far this year.
The multiple choice section will consist of approximately 30-35 questions.
____
1. Are points A, C, D and F coplanar? Explain.
a.
b.
c.
d.
Yes; they all lie on plane P.
No; they are not on the same line.
Yes; they all lie on the same face of the pyramid.
No; three lie on the same face of the pyramid and the fourth does not.
Refer to Figure 2.
Figure 2
____
____
____
2. How many planes are shown in the figure?
a. 4
c. 5
b. 3
d. 6
3. How many planes contain points B, C, and A?
a. 1
c. 0
b. 2
d. 3
4. Where could you add point M on plane LBD so that D, B, and M would be collinear?
←
→
a.
anywhere on DF
b.
anywhere on LD
←

→
c.
anywhere on BL
d.
anywhere on BD
←

→
←
→
1
Name: ________________________
____
____
ID: A
5. Name an intersection of plane GFL and the plane that contains points A and C.
a. line LC
c. line AC
b. C
d. plane CAB
6. Find the value of the variable and GH if H is between G and I.
GI = 5b + 1,HI = 4b − 5,HI = 7
a.
b.
b = 1.2, GH = 6.8
b = 1.22, GH = 7.11
c.
d.
b = 3, GH = 9
b = 3, GH = 16
Use the Distance Formula to find the distance between each pair of points.
____
7.
a.
b.
50
34
c.
6
d.
4
Find the coordinates of the midpoint of a segment having the given endpoints.
____
8. Q −0.4, 2.5 , R 3.5, 1.5
a.
1.55, 2
c.
−1.95, 0.5
b.
1.05, 2.5
d.
−3.9, 1
2
Name: ________________________
ID: A


→
In the figure, GK bisects ∠FGH .
9. If m∠FGK = 3v − 4 and m∠KGH = 2v + 7, find x.
a. 33
c.
b. 58
d.
____ 10. If m∠FGK = 7w + 3 and m∠FGH = 104, find w.
a. 7
c.
b. 14.43
d.
____


→

→
11
29
52
3.5

→
In the figure, KJ and KL are opposite rays. ∠1 ≅ ∠2 and KM bisects ∠NKL.

→
____ 11. Which is NOT true about KM ?
a. ∠MKJ is acute.
b. ∠3 ≅ ∠MKL
c. Point M lies in the interior of ∠LKN .
d. It is an angle bisector.
____ 12. If m∠LKN = 7q + 2 and m∠4 = 4q − 5, what is m∠3?
a. 137
c. 4.2
b. 12
d. 43
____ 13. The measures of two complementary angles are 12q − 9 and 8q + 14. Find the measures of the angles.
a. 42, 48
c. 8.75
b. 4.25
d. 96, 84
____ 14. Find m∠Y if m∠Y is six more than three times its complement.
a. 136.5
c. 21
b. 43.5
d. 69
3
Name: ________________________
ID: A
____ 15. The measure of an angle’s supplement is 24 less than twice the measure of the angle. Find the measure of the
angle and its supplement.
a. 38, 52
c. 68, 112
b. 52, 38
d. 112, 68
____ 16. Rays AB and BC are perpendicular. Point D lies in the interior of ∠ABC . If m∠ABD = 4r − 7 and
m∠DBC = 8r + 1, find m∠ABD and m∠DBC .
a. 8, 90
c. 21, 69
b. 55, 125
d. 25, 65
____ 17. If m∠BEF = 3 h − 4 and m∠FED = 2h − 23, find h such that BE ⊥ ED .
a. 23.4
c. 9
b. 25
d. 43
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
____ 18. Given: points A, B, C, and D
Conjecture: A, B, C, and D are coplanar.
a. False; the four points do not have to be in a straight line.
b. True
c. False; two points are always coplanar but four are not.
d. False; three points are always coplanar but four are not.
____ 19. Given: point B is in the interior of ∠ADC .
Conjecture: ∠ADB ≅ ∠BDC
a. False; m∠ADB may be obtuse.
b. True
c. False; just because it is in the interior does not mean it is on the bisecting line.
d. False; m∠ADB + m∠BDC = 90.
____ 20. Given: m2 + 6 = 10
Conjecture: m = 2
a. False; m = 4.
c. False; m = 3.
b. True
d. False; m = −2.
____ 21. Given: ∠ABC, ∠DBE are coplanar.
Conjecture: They are vertical angles.
a. False; the angles may be supplementary.
b. True
c. False; one angle may be in the interior of the other.
d. False; the angles may be adjacent.
Write the statement in if-then form.
____ 22. Spiders can walk on walls.
a. If it can walk on walls, then it can walk on walls.
b. If it is a spider, then it can walk on walls.
c. If it is a spider, then it is a spider.
d. If it can walk on walls, then it is a spider.
4
Name: ________________________
ID: A
Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false,
find a counterexample.
____ 23. If you have a dog, then you are a pet owner.
a. If you are a pet owner, then you have a dog. True
b. A dog owner owns a pet. True
c. If you are a pet owner, then you have a dog. False; you could own a hamster.
d. If you have a dog, then you are a pet owner. True
Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false,
find a counterexample.
____ 24. All quadrilaterals are four-sided figures.
a. All non-quadrilaterals are four-sided figures. False; a triangle is a non-quadrilateral.
b. All four-sided figures are quadrilaterals. True
c. No quadrilaterals are not four-sided figures. True
d. No four-sided figures are not quadrilaterals. True
Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If
it is false, find a counterexample.
____ 25. If you are 16 years old, then you are a teenager.
a. If you are not a teenager, then you are not 16 years old. True
b. If you are not 16 years old, then you are not a teenager. False; you could be 17 years old.
c. If you are not a teenager, then you are 16 years old. True
d. If you are a teenager, then you are 16 years old. False; you could be 17 years old.
____ 26. Two angles measuring 180 are supplementary.
a. Two angles not measuring 180 are not supplementary. True
b. More than two angles measuring 180 are non-supplementary. True
c. Non-supplementary angles are not two angles measuring 180. True
d. Non-supplementary angles are two angles measuring 180. False; supplementary angles
must measure 180.
Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of
Syllogism. If it does, state which law was used. If it does not, write invalid.
____ 27. (1) You are in ninth grade.
(2) People who are in ninth grade floss their teeth regularly.
(3) You floss your teeth regularly.
a. yes; Law of Syllogism
b. invalid
c. yes; Law of Detachment
5
Name: ________________________
ID: A
____ 28. In the figure, AB CD. Find x and y.
x = 32, y = 140
x = 140, y = 52
____ 29. In the figure, p q . Find m∠1.
c.
d.
x = 52, y = 140
x = 38, y = 154
m∠1 = 61
m∠1 = 35
c.
d.
m∠1 = 55
m∠1 = 64
a.
b.
a.
b.
Determine the slope of the line that contains the given points.
____ 30. T −6, 0 , V 5, 3
a.
b.
3
11
1
−
3
c.
d.
6
11
3
11
3
−
Name: ________________________
←

→
ID: A
←

→
Determine whether WX and YZ are parallel, perpendicular, or neither.
____ 31. W −2, − 1 , X 4, 1 , Y 1, − 4 , Z 5, − 4
a.
b.
c.
perpendicular
parallel
neither
Write an equation in slope-intercept form of the line having the given slope and y-intercept.
____ 32. m: −
a.
b.
4
, 0, − 3
5
12
y=
x
5
4
y = − x−3
5
c.
y = −3x −
d.
3
y=− x
5
4
5
Write an equation in point-slope form of the line having the given slope that contains the given point.
2 15
1
,−
____ 33. m = − ,
3
4
2
a.
y+
1
2
15
=− x−
2
3
4
c.
y+
1
2
15
=− x+
2
3
4
b.
y−
15
2
1
=− x+
4
3
2
d.
2
41
y =− x+
3
12
Determine which lines are parallel. State the postulate/theorem that justifies your answer.
____ 34. ∠11 ≅ ∠2
a.
b.
c.
d.
c
a
c
a
d ; congruent corresponding angles
b ; congruent corresponding angles
d ; congruent alternate interior angles
b ; congruent alternate interior angles
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Name: ________________________
ID: A
____ 35. ∠LHO ≅ ∠NKP
a.
b.
c.
d.
c
a
a
c
d ; congruent corresponding angles
b ; congruent corresponding angles
b ; congruent alternate exterior angles
d ; congruent alternate exterior angles
8
Name: ________________________
ID: A
Construct a line perpendicular to m through P. Then find the distance from P to m.
____ 36. Line m contains points 3, 1 and 1, 1 . Point P has coordinates 5, 2 .
a.
c.
d=1
b.
d=2
d.
d=1
d=5
Find the distance between the pair of parallel lines.
____ 37. y = 4x + 4
4x − y = 1
a. d = 1.64
b. d = 1.47
c.
d.
d = 1.21
d = 1.28
Find the measures of the sides of ∆ABC and classify the triangle by its sides.
____ 38. A 5, − 2 , B 7, 2 , C 3, 5
a.
b.
equilateral
isosceles
c.
d.
9
scalene
obtuse
Name: ________________________
ID: A
Find each measure.
____ 39. m∠1, m∠2, m∠3
a. m∠1 = 77, m∠2 = 41, m∠3 = 37
b. m∠1 = 77, m∠2 = 36, m∠3 = 30
____ 40. m∠1, m∠2, m∠3
a.
b.
m∠1 = 74, m∠2 = 129, m∠3 = 101
m∠1 = 46, m∠2 = 129, m∠3 = 129
c.
d.
m∠1 = 82, m∠2 = 41, m∠3 = 37
m∠1 = 82, m∠2 = 92, m∠3 = 30
c.
d.
m∠1 = 51, m∠2 = 101, m∠3 = 101
m∠1 = 74, m∠2 = 152, m∠3 = 74
Determine whether ∆PQR ≅ ∆STU given the coordinates of the vertices. Explain.
____ 41. P 3, − 2 , Q 1, 2 , R −1, 4 , S −4, − 3 , T −2, 1 , U 0, 3
a.
b.
c.
d.
Yes; each side of triangle PQR is the same length as the corresponding side of triangle
STU.
No; each side of triangle PQR is not the same length as the corresponding side of triangle
STU.
No; two sides of triangle PQR and angle PQR are not the same measure as the
corresponding sides and angle of triangle STU.
Yes; both triangles have three sides.
10
Name: ________________________
ID: A
Refer to the figure. ∆ARM, ∆MAX, and ∆XFM are all isosceles triangles.
____ 42. What is m∠RAM ?
a. 23
c. 42
b. 38
d. 35
____ 43. What is m∠AMX ?
a. 80
c. 64
b. 38
d. 72
____ 44. What is m∠MAX ?
a. 16
c. 36
b. 38
d. 108
____ 45. Triangle FJH is an equilateral triangle. Find x and y.
7
7
a.
x = 5 , y = 16
c.
x = 5 , y = 14
b.
x = 7, y = 16
d.
x = 7, y = 14
____ 46. Triangle RSU is an equilateral triangle. RT bisects US . Find x and y.
1
a.
x = − 3 , y = 32
b.
x = 2 , y = 62
1
1
c.
x = 3 , y = 62
d.
x = 2 , y = 32
11
1
Name: ________________________
ID: A
____ 47. Triangles ABC and AFD are vertical congruent equilateral triangles. Find x and y.
c. x = 1, y = 10
x = 1, y = 5
d. x = 7, y = 5
x = 7, y = 10
____ 48. Lines s, t, and u are perpendicular bisectors of ∆FGH and meet at J. If JG = 4x + 3, JH = 2y − 3, JF = 7 and
HI = 3z − 4 , find x, y, and z.
a.
b.
a.
b.
x = 1, y = 5, z = 5
x = 2.5, y = 2, z = 2.3
c.
d.
x = 5, y = 1, z = 5
x = 0, y = 6, z = 2.3
____ 49. RU is an angle bisector. ∠RTU = 13x − 24, ∠TRS = 12x − 34, and ∠RUS = 92. Find m∠RSU . Is RU ⊥ TS ?
a.
b.
63; No
65; No
c.
d.
60; Yes
29; No
____ 50. d XW is an angle bisector. ∠WZX = 5x + 11, ∠ZXW = 6x − 10, and ∠XWZ = 91. Find m∠WXY .
a.
b.
40
35
c.
d.
12
38
30
Name: ________________________
ID: A
____ 51. XW is an angle bisector. ∠YXZ = 9x + 38, ∠WXY = 10x − 14, ∠XZY = 8x. Find m∠WZX . Is XW an altitude?
a.
b.
45; Yes
48; No
c.
d.
32; No
52; No
Determine the relationship between the measures of the given angles.
____ 52. ∠PTC, ∠VPT
a. ∠PTC > ∠VPT
b. ∠PTC < ∠VPT
____ 53. ∠JCQ, ∠RCQ
a.
b.
∠JCQ > ∠RCQ
∠JCQ < ∠RCQ
c.
∠PTC = ∠VPT
c.
∠JCQ = ∠RCQ
13
Name: ________________________
ID: A
Determine the relationship between the lengths of the given sides.
____ 54. HB, BL
a.
b.
HB > BL
HB = BL
c.
d.
cannot be determined
HB < BL
Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.
____ 55. 9.2, 14.5, 17.1
a. Yes; the third side is the longest.
b. No; the first side is not long enough.
c. Yes; the sum of the lengths of any two sides is greater than the third.
d. No; the sum of the lengths of two sides is not greater than the third.
____ 56. An isosceles triangle has a base 9.6 units long. If the congruent side lengths have measures to the first
decimal place, what is the shortest possible length of the sides?
a. 4.9
c. 4.7
b. 19.3
d. 9.7
____ 57. Find the measure of an interior angle of a regular polygon with 14 sides. Round to the nearest tenth if
necessary.
a. 2160
c. 154.3
b. 25.7
d. 360
____ 58. Find the measure of each exterior angle for a regular nonagon. Round to the nearest tenth if necessary.
a. 1260
c. 360
b. 140
d. 40
14
Name: ________________________
ID: A
Complete the statement about parallelogram ABCD.
____ 59. ∠CDA ≅ ____
a. ∠ABC ; Alternate interior angles are congruent.
b. ∠ACD; Alternate interior angles are congruent.
c. ∠ABC ; Opposite angles of parallelograms are congruent.
d. ∠ACD; Opposite angles of parallelograms are congruent.
Refer to parallelogram ABCD to answer to following questions.
____ 60. What is the length of segment AK?
a.
34
b.
2 34
c.
d.
15
3 2
6 2
Name: ________________________
ID: A
Refer to parallelogram ABCD to answer the following questions.
____ 61. Do the diagonals bisect each other? Justify your answer.
a. yes; AK ≅ CK and DK ≅ BK .
b. yes; The diagonals are not congruent.
c. no; AK ≅ CK and DK ≅ BK .
d. no; The diagonals are not congruent.
Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.
____ 62. A(1, − 6), B(−1, − 3) , C(−2, 7), D(0, 4) ; Slope Formula
a. yes; The opposite sides have the same slope.
b. no; Opposite sides are the same length.
c. no; The opposite sides have the same slope.
d. yes; Opposite sides are the same length.
____ 63. A(3, − 9), B(10, 1) , C(4, 10), D(−9, 3) ; Distance and Slope Formulas
a. no; The opposite sides are not congruent and do not have the same slope.
b. yes; The opposite sides do not have the same slope.
c. no; The opposite sides do not have the same slope.
d. yes; The opposite sides are not congruent and do not have the same slope.
Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square.
List all that apply.
____ 64. A(5, 10), B(4, 10) , C(4, 9), D(5, 9)
a. square; rectangle; rhombus
b. rhombus
____ 65. A(−2, 6), B(−2, − 1) , C(−9, − 1), D(−9, 6)
a. rhombus
b. square; rectangle; rhombus
c.
d.
square
rectangle
c.
d.
square
rectangle
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