Download Geometry Formula Sheet First Semester Exam Slope: Midpoint

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 70 true false and 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 separate sheets of paper, and you must show work
on starred (***) problems. I WILL NOT ACCEPT LATE REVIEWS!
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.
There will be a few days in class to work on these as well. Here is the exam schedule.
8:20
9:00
9:45
10:30
11:00
11:35
1:35
- 8:55
- 9:40
- 10:25
- 11:00
- 11:30
- 1:30
- 3:20
Tue, Jan 11
Period 1
Period 2
Period 3
Period 7 (1st lunch)
Period 7 (2nd lunch)
Period 7 Exam
Make-up Work
Wed, Jan 12
8:20
10:30
11:00
11:35
1:35
- 10:20
- 11:00
- 11:30
- 1:30
- 3:20
Period 1 Exam
Period 2 Exam
Period 4 (1st lunch) Period 5 (1st lunch)
Period 4 (2nd lunch) Period 5 (2nd lunch)
Period 4 Exam
Period 5 Exam
Make-up Exam
Make-up Exam
You will be given the following formula sheet for your exam:
Geometry Formula Sheet
First Semester Exam
Slope:
Midpoint:
Distance:
Point Slope Form of a Line:
Slope Intercept Form of a Line:
Thu, Jan 13
Fri, Jan 14
Period 3 Exam
Period 6 (1st lunch)
Period 6 (2nd lunch)
Period 6 Exam
Make-up Exam
Review Questions: To be done on separate sheets of paper (it is not necessary to copy
problems, but work must be shown on starred (***) problems.) 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 – list all of them.) (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
. (1)
20. Sketch triangle ABC with median
21. Sketch triangle MNP with altitude
. (5)
. (5)
22. Sketch triangle XYZ with angle bisector
. (5)
23. Sketch triangle KLM with the perpendicular bisector of LN . (5)
24. Sketch a triangle RST with a midsegment parallel to
(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 ΔMNP ≅ ΔQRS , 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. (1)
39. *** Find the slope of the line connecting the points (4, -1) and (-2, 6). Write it as a
reduced fraction. (3)
40. What is the slope of a line parallel to the line in #39? (3)
41. What is the slope of a line perpendicular to the line in #39? (3)
42. *** Find the midpoint of the segment connecting (3, 1) and (-5, -2). (1)
43. *** A is (1, 4) and M is (3, -2). If M is the midpoint of
, find the coordinates of
B. (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)
50. Using the figure at the right, name the transversal. (3)
51. Name a pair of corresponding angles. (3)
52. Name a pair of alternate interior angles. (3)
53. Name a pair of alternate exterior angles. (3)
54. Name a pair of same-side interior angles. (3)
55. Name a linear pair. (1)
56. Name a pair of vertical angles. (1)
57. In ΔABC, m∠A = 30 and m∠B = 130. Sketch the triangle, find
and list the
sides in increasing order. (5)
58. In ΔMNF, 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. (2)
61. *** The three angles of a triangle have measures of x + 8, 2x, and 8x – 15. Find the
measure of each angle. (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, find x in reduced radical form. Show work. (All in chapter 5.)
*66.
*67.
x
20
3
x
4
6
*68.
*69.
16
x
18
30
x
15
In the figure at the right, B, F, and D are midpoints. (Ch. 5)
A
70. CE = ?
4cm
71. FD = ?
72. BD = ?
3cm
B
73. m∠E = ?
74. m∠BDF = ?
55°
75. m∠DFB = ?
65°
C
D
Tell whether each represents a translation, reflection, or rotation. (Ch 1)
76.
77.
78.
F
12 cm
E
A
79. Complete the following proof. (Ch. 4)
1 2
≅
Given:
1.
,
≅
Prove: ∠P ≅ ∠Q
Statements
≅
,
≅
3 4
P
M
Q
Reasons
1.
2.
2.
3. ΔAPM ≅ ΔAQM
3.
4. ∠P ≅ ∠Q
4.
80. In the following proof, the statements are in the wrong order. List the correct order.
(Ch. 4)
Given:
≅
, ∠D and ∠X are right angles,
∠E ≅ ∠Y
Y
E
Prove: ∠1 ≅ ∠2
D
Statements
A. ΔEFD ≅ ΔYZX
B. ∠1≅ ∠2
C.
≅
D. ∠D ≅ ∠X
, ∠D and ∠X are right angles, ∠E ≅ ∠Y
1
Z
2
F
X