Geometry Midterm 1 - 5 STUDY GUIDE
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
1. Is the line through points P(–7, –6) and Q(0, –9) parallel to the line through points R(0, 1) and S(–1, 3)? Explain.
a. No, the lines have unequal slopes.
b. Yes; the lines are both vertical.
c. No, one line has slope, the other has no slope.
d. Yes; the lines have equal slopes.
2. Is the line through points P(–7, –6) and Q(–5, –14) perpendicular to the line through points R(2, –10) and S(4,
–2)? Explain.
a. Yes; their slopes have product –1
b. Yes; their slopes are equal.
c. No, their slopes are not reciprocals.
d. Yes; their slopes have product –1
3. Based on the given information, what can you conclude, and why?
Given:
I
K
J
H
|
A
B
D
|
____
L
a.
by ASA
c.
by SAS
b.
by ASA
d.
by SAS
4. Name the theorem or postulate that lets you immediately conclude
C
a. SAS
b. ASA
c. AAS
d. none of these
____
5. Supply the missing reasons to complete the proof.
Given:
and
Prove:
I
K
J
H
____
L
a. ASA; Substitution
c. SAS; CPCTC
b. AAS; CPCTC
d. ASA; CPCTC
6. Which three lengths could be the lengths of the sides of a triangle?
a. 19 cm, 7 cm, 8 cm
c. 8 cm, 15 cm, 22 cm
b. 14 cm, 7 cm, 21 cm
d. 9 cm, 24 cm, 11 cm
Short Answer
7. Find the distance between points P(7, 6) and Q(5, 8) to the nearest tenth.
8. Find the coordinates of the midpoint of the segment whose endpoints are H(4, 11) and K(2, 13).
9. Ralph wants to put a fence around his rectangular garden. His garden measures 39 feet by 53 feet. The garden
has a path around it that is 3 feet wide. How much fencing material does Ralph need to enclose the garden and
path?
10. Find the circumference of the circle to the nearest tenth.Use 3.14 for .
25 m
11. Find the area of the circle in terms of .
44 in.
12. Find, to the nearest tenth, the area of the region that is inside the square and outside the circle. The circle has
diameter 4 inches.
13. Supplementary angles are two angles whose measures have sum ____.
Complementary angles are two angles whose measures have sum ____.
14. Find the values of x and y.
4y°
2x – 6°
128°
Drawing not to scale
15. Line r is parallel to line t. Find m 5. The diagram is not to scale.
r
7
145°
1
t
3
4
2
5
6
16. Find the value of the variable if
1
2
3
and
l
4
5
6
7
m
8
17. Find the value of x. The diagram is not to scale.
46°
131°
x°
18. Find the value of the variable. The diagram is not to scale.
117°
51°
x°
19. Find
. The diagram is not to scale.
96°
118°
115°
104°
A
The diagram is not to scale.
20. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to
scale.
d°
24°
g
5
b
f°
e°
4
66°
3
c
21. Justify the last two steps of the proof.
Given:
and
Prove:
M
N
O
P
Proof:
1.
2.
3.
4.
1. Given
2. Given
3.
4.
22. From the information in the diagram, can you prove
? Explain.
23. Find the values of x and y.
(
(
A
|
|
y°
x°
B
68°
D
C
Drawing not to scale
24. Use the information in the figure. Find
|
E
|
D
108°
F
Drawing not to scale
25. Find the value of x. The diagram is not to scale.
38
x
38
26
23
23
26. Q is equidistant from the sides of
Find the value of x. The diagram is not to scale.
|
|
T
|
Q
(4
)°
|
9
x+
29°
R
S
27. Name a median for
|
C
G
) |
F
)
E
H D
28. Name the point of concurrency of the angle bisectors.
29. What is the name of the segment inside the large triangle?
30. For the two quadrilaterals below,
congruence statement for the two quadrilaterals.
___?___
31. Prove:
.
A
B
|
|
D
(
(
C
32.
Given:
Prove:
Q
R
P
S
and
Complete this
33. Given:
is the perpendicular bisector of IK. Name two lengths that are equal.
A
I
K
J
B
34. Find the values of x, y, and z. The diagram is not to scale.
44°
14°
58°
x°
z°
y°
35. List the sides in order from shortest to longest. The diagram is not to scale.
J
23°
77°
K
80°
L
36. Write an equation for the line parallel to y = -2x + 15 that contains P(8, -6).
Other
37. Line p contains points A(–6, 1) and B(2, –4). Line q is parallel to line p. Line r is perpendicular to line q. What
is the slope of line r? Explain.
38. T is the midpoint of QR. U is the midpoint of QS. RS = 36 and mQUT = 85. What are TU and mQSR?
Explain.
Q
T
R
U
S
39. Two sides of a triangle have lengths 6 and 8. What lengths are possible for the third side? Explain.
Geometry Midterm 1 - 5 STUDY GUIDE
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
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3-6 Slopes of Parallel and Perpendicular Lines
TOP:
3-6 Slopes of Parallel and Perpendicular Lines
TOP:
4-3 Triangle Congruence by ASA and AAS
TOP:
4-3 Triangle Congruence by ASA and AAS
TOP:
4-4 Using Congruent Triangles: CPCTC
TOP:
5-5 Inequalities in Triangles
TOP: 5-5 Example 4
3-6 Example 1
3-6 Example 4
4-3 Example 4
4-3 Example 2
4-4 Example 1
SHORT ANSWER
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1-6 The Coordinate Plane
TOP: 1-6 Example 1
1-6 The Coordinate Plane
TOP: 1-6 Example 3
1-7 Perimeter, Circumference, and Area
TOP:
1-7 Perimeter, Circumference, and Area
TOP:
1-7 Perimeter, Circumference, and Area
TOP:
1-7 Perimeter, Circumference, and Area
TOP:
2-5 Proving Angles Congruent
TOP: 2-5 Example 1
2-5 Proving Angles Congruent
TOP: 2-5 Example 4
3-1 Properties of Parallel Lines
TOP: 3-1 Example 4
3-1 Properties of Parallel Lines
TOP: 3-1 Example 5
3-3 Parallel Lines and the Triangle Angle-Sum Theorem TOP:
3-3 Parallel Lines and the Triangle Angle-Sum Theorem
3-4 The Polygon Angle-Sum Theorems
4-1 Congruent Figures
TOP: 4-1 Example 1
4-2 Triangle Congruence by SSS and SAS
TOP:
4-3 Triangle Congruence by ASA and AAS
TOP:
4-5 Isosceles and Equilateral Triangles
TOP:
4-5 Isosceles and Equilateral Triangles
TOP:
5-1 Midsegments of Triangles
TOP: 5-1 Example 1
5-2 Bisectors in Triangles
TOP: 5-2 Example 2
5-3 Concurrent Lines, Medians, and Altitudes
TOP:
5-3 Concurrent Lines, Medians, and Altitudes
5-3 Concurrent Lines, Medians, and Altitudes
TOP:
4-1 Congruent Figures
TOP: 4-1 Example 1
4-4 Using Congruent Triangles: CPCTC
TOP:
4-4 Using Congruent Triangles: CPCTC
TOP:
5-2 Bisectors in Triangles
TOP: 5-2 Example 1
3-3 Parallel Lines and the Triangle Angle-Sum Theorem TOP:
5-5 Inequalities in Triangles
TOP: 5-5 Example 3
1-7 Example 1
1-7 Example 2
1-7 Example 5
1-7 Example 6
3-3 Example 4
4-2 Example 1
4-3 Example 3
4-5 Example 3
4-5 Example 3
5-3 Example 4
5-3 Example 4
4-4 Example 2
4-4 Example 2
3-3 Example 2
OTHER
37. REF: 3-6 Slopes of Parallel and Perpendicular Lines
38. REF: 5-1 Midsegments of Triangles
39. REF: 5-5 Inequalities in Triangles