Download Geometry Semester Exam Information:

Geometry Semester Exam Information:
The semester exam will cover material from chapters 1-5. It will be worth 20% of your
first semester grade. It consists of about 70 true false or multiple choice questions.
Studying previous tests and quizzes is an excellent way to prepare, as well as doing the
attached study guide. The attached questions must be turned in on the day of your exam
(as you arrive at class.) They must be done neatly on a separate sheet of paper, with
necessary work shown. I will not accept work that is sloppily done, nor will I accept
work late. These review questions will be worth 10% of your exam grade. You need to
start preparing now so you have time to look up and ask about problems you don’t
understand.
You will be given the following formula sheet for your exam:
Geometry Formula Sheet
First Semester Exam
Slope:
m
Midpoint:
Distance:
y2  y1
x2  x1
 x1  x2 y1  y2 
,


2 
 2
D
 x2  x1    y2  y1 
2
2
Point Slope Form of a Line: y  y1  m  x  x1 
Slope Intercept Form of a Line: y  mx  b
Review Questions: To be done on a separate sheet of paper (it is not necessary to copy
problems, but work must be shown as indicated.) The number in parentheses at the end
of the problem tells which chapter it comes from.
1.
2.
3.
4.
5.
6.
7.
8.
9.
____ points are always collinear (give the largest number.) (1)
____ points are always coplanar (give the largest number.) (1)
What figure is formed by the intersection of two lines? (1)
What figure is formed by the intersection of two planes? (1)
What figure is formed by the intersection of a line and a plane? (1)
Define supplementary and complimentary angles. (1)
What is special about two angles that form a linear pair? (2)
What is special about vertical angles? (2)
When two lines are parallel and cut by a transversal, which angle pairs are congruent?
Which are supplementary? (Multiple answers.) (3)
10. A ____ triangle has no congruent sides. (4)
11. A ____ triangle has at least two congruent sides. (4)
12. A ____ triangle has all sides congruent. (4)
13. What is significant about the angles in an isosceles triangle? (4)
14. What is significant about the angles in an equilateral triangle (be as specific as
possible)? (4)
15. Could a triangle have sides of length 2, 3, and 4? Justify your answer. (5)
16. Could a triangle have sides of length 15, 15, 30? Justify your answer. (5)
17. Could a triangle have sides of length 4, 5, and 10? Justify your answer. (5)
18. What are the possible lengths of the third side of a triangle with sides 20 and 30? (5)
19. Explain the difference between the notations AB, AB, AB, AB . (1)
20. Sketch triangle ABC with median BD . (5)
21. Sketch triangle MNP with altitude PQ . (5)
22. Sketch triangle XYZ with angle bisector XW . (5)
23. Sketch triangle KLM with the perpendicular bisector of LM . (5)
24. Sketch a triangle RST with a midsegment parallel to ST (5)
25. Consider SSS, SAS, ASA, AAS, SSA, AAA, HL? Which of them can be used to
prove triangles are congruent? Which cannot be? (4)
26. Consider the conditional statement “If x = y, then a = b.” Write the converse, inverse,
and contrapositive. (2)
27. If a conditional statement is true, what else must be true? (2)
28. If the converse of a statement is true, what else must be true? (2)
S
R
29. In the figure at the right, name two pairs of supplementary angles. (1)
30. Name two pairs of complementary angles. (1)
45
31. Name two pairs of adjacent angles. (1)
W  90
32. Name one pair of vertical angles. (1)

33. Name two linear pairs. (1)
45 45
Q
34. If MNP  QRS , name all pairs of congruent sides and angles. (4)
 
T
35. Write down the distance formula. (1)
P
36. Write down the slope formula. (3)
37. Write down the midpoint formula. (1)
38. Find the distance between the points (3, 2) and (-1, 4) Round to the nearest
hundredth. Show work. (1)
39. Find the slope of the line connecting the points (4, -1) and (-2, 6). Write it as a
reduced fraction. Show work. (3)
40. What is the slope of the line parallel to the line in # 39? (3)
41. What is the slope of the line perpendicular to the line in # 39? (3)
42. Find the midpoint of the segment connect (3, 1) and (-5, -2). Show work. (1)
43. A is (1, 4) and M is (3, -2). If M is the midpoint, of AB , find the coordinates of B.
Show work. (1)
44. In the figure at the right, are S, Q, R, and V coplanar? (1)
45. Name the marked points in both planes A and B. (1)
46. What is the intersection of planes A and B. (1)
47. Name two points collinear with V. (1)
48. What does CPCTC stand for? (4)
49. Explain the concept of CPCTC. (4)
a
50. Using the figure at the right, name the transversal. (3)
b
51. Name a pair of corresponding angles. (3)
2
1
52. Name a pair of alternate interior angles. (3)
4
3
53. Name a pair of alternate exterior angles. (3)
c
6
5
54. Name a pair of same-side interior angles. (3)
8
7
55. Name a linear pair. (1)
56. Name a pair of vertical angles. (1)
57. In ABC , mA  30 and mB  130. Sketch the triangle, find mC and list the
sides in increasing order. (5)
58. In MNP , MN = 5, NP = 10, and MP = 13. Sketch the triangle and list the angles in
increasing order. (5)
59. The exterior angle at the base of an isosceles triangle is 150. Find the measures of all
three interior angles. (4)
60. Two angles that form a linear pair have measures of 3x + 5 and 7x + 25. Find the
measure of each angle. Show work. (2)
61. The three angles of a triangle have measures of x + 8, 2x, and 8x – 15. Find the
measure of each angle. Show work. (4)
62. Find the equation of a line, in point-slope form, that passes through (3, 2) and (-1, 8)
(3)
63. Find the equation of a line, in slope-intercept form, that has a slope of -3 and passes
through (3, -2). (3)
64. Determine whether the lines 2x + 3y = 9 and 4x + 6y = 18 are parallel, perpendicular,
intersecting but not perpendicular, or coincident. (3)
65. Determine whether the lines y = 2x + 1 and 4x – 2y = 8 are parallel, perpendicular,
intersecting but not perpendicular, or coincident. (3)
In the following problems, give the reason the triangles are congruent (SAS, SSS, etc)
and the congruency statement. It is possible that the triangles are not congruent. (4)
66.
X
B
67.
B
D
Y
C
D
C
Z
E
F
68.
A
X
69. MK bisects <JML, <J  <L
M
C
B
Y
Z
J
70. RS  UT , TU bisects RTS
71.
K
L
A
R
D
C
T
U
B
E
S
72. Q is the midpoint of NT and PS
N
S
Q
P
73.
T
A
10 cm
D
B
10 cm
C
74-77 do not exist
In the figure at the right, B, F, and D are midpoints. (ch 5)
A
78. CE = ?
4cm
79. FD = ?
80. BD = ?
3cm
81. m<E = ?
B
82. m<BDF = ?
55
83. m<DFB = ?
°
65
C °
D
Tell whether each represents a translation, reflection, or rotation. (Ch 1)
84.
85.
86.
12 cm
F
E
A
87. Complete the following proof. (ch 4)
1 2
Given: PM  QM , AP  AQ
Prove: <P  <Q
statements
1. PM  QM , AP  AQ
1.
2. AM  AM
2.
3. APM  AQM
3.
4. <P  <Q
4.
3 4
M
P
Q
reasons
88. In the following proof, the statements are in the wrong order. List the correct order.
(ch 4)
Given: EF  YZ , <D and <X are right angles,
<E  <Y
Y
E
Prove: <1  <2
1
statements
A. EFD  YZX
.
B. <1 <2
C. EF  YZ , <D and <X are right angles, <E  <Y
D. <D  <X
D
Z
2
F
X