Download Geometry Midter Study Guide

Geometry Midterm Exam - Study Guide
Name:__________________
1. a. What is the exact distance between P and M? Explain.
b. If the distance between Q and N is 42, what is x? Justify your answer.
c. If the distance between Q and N is 3.5x, what is x? Justify your answer.
2. a. What are the approximate lengths of
and
?
b. Find the midpoint of each segment. What is true about the midpoints?
3. m SQR = (
)° and m PQR = (
Find m SQR and m PQR.
4.
and
are opposite rays.
)° and m SQP = 70°.
bisects
.
°. Draw a sketch and find
.
5. Write a definition for supplementary angles.
6. Look at the set of dots below. Sketch the next figure, and predict the total number of dots in the 6th figure.
7. Give one counterexample that shows the conjecture is false:
In a coordinate plane, if the x-coordinate of a point is positive, then the point is in the first quadrant.
8. "If an obtuse angle is bisected, then two acute angles are obtained."
Decide whether the statement and its converse are true. If false, explain.
9. Refer to the following statement:
Two lines are perpendicular if and only if they intersect to form a right angle.
A. Is this a biconditional statement?
B. Is the statement true?
10. Given the following statements, can you conclude that Marvin listens to the radio on Monday night?
(1) If it is Monday night, Marvin stays at home.
(2) If Marvin stays at home, he listens to the radio.
11. Explain the difference between inductive and deductive reasoning.
Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your reasoning.
12. For the past 6 weeks, your aunt has asked you to watch your cousin on Wednesday night. You conclude that you will be
asked to watch your cousin next Wednesday.
13. Sketch a diagram showing the following:
Line m is perpendicular to segment AB at P, the midpoint of segment AB.
14. You want to know the number of minutes that you can use on your $15.00 phone card. The card company charges you $1.00
for the first minute and $0.20 for each additional minute. Solve the formula
for m. Justify each step
with an algebraic property of equality.
15. Identify the property that makes the statement true.
If m 1 + m 2 = 25° and m 1 = 9°, then
.
16. Provide the reasons for each statement in the proof.
Given:
Prove:
17.
are supplementary angles.
are vertical angles.
. Find
.
18. True or False: If two angles are supplements of the same angle, then they must be equal in measure.
19.
1 and 2 are complementary, and 2 and 3 form a linear pair. If m 1 =
20. Define skew lines.
, what is m 3? Explain your reasoning.
21. Given: Lines q and r are parallel.
Transversal t intersects lines q and r.
Prove:
are supplementary.
Statements:
22. Lines a and b in the figure below are parallel. What is the measure of
Reasons:
in degrees?
23. Which lines, if any, can be proved parallel given the following diagram?
24. a) Calculate the slope of the line. Does it matter which points are used? Why?
b) Write the equation of the line parallel to the given one and passing through
point (−2, 4).
c) Write the equation of the line perpendicular to the given one and passing through
point (4, −6).
25. Writing: Explain the difference between a horizontal line and a vertical line in terms of slope.
26. Find the distance between the point with coordinates (-1, 3) and the line with equation
.
27. Write an equation in slope-intercept that passes through points with coordinates (3, -4) and (-2, 1).
28. Tell whether lines m and n are parallel or not parallel and explain.
29. Solve for x, given that
. Is
equilateral?
30. How many acute angles can an isosceles triangle have? Explain.
31. Find the value of x.
32. Find the measure of exterior angle A.
33.
Solve for x.
34. A triangle has the given vertices. Classify the triangle by its sides. Then determine if it is a right triangle.
35. In
and
,
A
X,
B
Y, and C
Z. Is it always true that ABC
36. Given:
Statements:
XYZ? Explain.
Reasons:
Prove:
37. Write a proof. Justify each statement.
Given:
Prove:
Statements:
38.
Given:
Prove:
Reasons:
Statements:
Reasons:
39. Is there enough information given to prove that the following pairs of triangles are congruent? Explain why or why not. If
not, describe what information could be added to guarantee congruence.
40. Describe the differences between the AAS Theorem and the ASA Postulate.
41. Line l is the perpendicular bisector of
. Find the value of x.
42.
Statements:
43.
and AEB
Reasons:
CDB. What conclusion can you make about
the sides of EBD? Justify your reasoning.
44. The incenter of a triangle is equidistant from the three ____ of the triangle.
45. For the given triangle, state the relationships between
46.
and
is the perpendicular bisector of
. If OM = 4 and LN = 6,
then LO =______ and MN =______. Explain your solutions.
.
47. The point of concurrency of the three medians of the triangle is called _______________.
48. Refer to the figure.
Given:
Which line is a perpendicular bisector in ABC?
49. Find AB. Is there enough information to show that D lies on the
vertical line that passes through B?
50. Find the value of x.
52. In
RST Q
51. Find the value of x.
is the centroid and SQ 32 . Find QW and SW.
53. Using the Triangle Inequality Theorem, solve for all possible values of x.
54. Two sides of a triangle have lengths 9 and 14. What are the possible lengths of the third side x?
55. Can the measurements 1.4 meters, 2.7 meters, and 9.3 meters be the lengths of the sides of a triangle?
56. List the sides of triangle BCD in order from greatest to least.
(The figure may not be drawn to scale.)
Complete:
57. If
x
m 7 ?
m
= , then
=
7
5
5
7
58. If
d
2
f
=
, then
= ?
f
3
3
59. You are asked to fence in a triangular playground. Two sides of the playground have lengths of 100ft and 200 ft.
What is the maximum total length of fence you could possibly need?
60. True or false:
The median and altitude of a triangle can never be the same line segment.
61. Mr. Jones has taken a survey of college students and found that 90 out of 106 students are liberal arts majors. If a college has
7596 students, what is the best estimate of the number of students who are liberal arts majors?
62. Find the geometric mean of 144 and 4.
63. The measures of the angles of a triangle are in the extended ratio of 7 : 9 : 20. Find the measures of the angles of
the triangle.
64. Find the perimeter of the actual object using the scale factor
shown on the blueprint.
65. Are the two triangles (not drawn to scale) similar?
If so, explain why they are.
66. Which triangle is not similar to any of the others?
67.
ABC and XYZ are similar with A = X, and B = Y. If AB, BC, and AC are 6 inches, 7 inches, and 13 inches,
respectively, and XY is 14 inches, find XZ.
68. Triangle ABC is similar to triangle DEF. The perimeter of
is 108 centimeters. What is the length of
69. A building casts a shadow 200 meters long. At the same time, a pole 4 meters high casts a shadow 20 meters long.
What is the height of the building?
70. Determine whether the triangles are similar.
If the are, write a similarity statement.
71. Use the diagram to answer the following questions:
How do you know that
is similar to
How do you know that
is similar to
Find MK.
Name one other triangle in the diagram that is similar to
72. If p q, solve for x.
73. Find AC.