Download Geometry Practice Midterm 2 Name

Geometry Practice Midterm 2
____
Name____________________________
1. The first three members of a sequence are shown. How many dots are in the fourth member of the
sequence?
a. 30
b. 16
c. 14
d. 7
____
2. Rewrite the statement in if-then form.
All isosceles triangles have two congruent sides.
a. A figure has two congruent sides if and only if it is an isosceles triangle.
b. If a figure is an isosceles triangle, then it has two congruent sides.
c. A figure is an isosceles triangle if and only if it has two congruent sides.
d. If a figure has two congruent sides, then it is an isosceles triangle.
____
3. "If
a.
b.
c.
d.
, I will succeed." In this conditional statement, the underlined portion is ________.
the hypothesis
the converse
the argument
the conclusion
4. 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?
From the given true statements, make a valid conclusion:
5. If Joshua works on Sunday, he will not work on Tuesday.
If Joshua does not work on Tuesday, he will not work on Wednesday.
6. If MP = PQ and PQ = QR, then MP = QR.
Identify the property that makes the statement true.
____
7. Let
be between
=
=
= 24
and
. Use the Segment Addition Postulate to solve for .
a.
=6
b.
=4
8. Find AB and BC in the situation shown.
AB = x + 16, BC = 5x + 10, AC = 56
____
9. Find the distance between the points (0, –5) and (3, 5).
c.
= –2
d.
= 10
a. 109
b.
109
c. 3
d. 9
____ 10. Find the midpoint of the segment with endpoints (7, 2) and (–5, 6).
a. (1, 4)
c. (5, –11)
b. (6, 2)
d. (2, 8)
____ 11. mPNO = (
)° and mMNO = (
Find mPNO and mMNO.
a.
b.
c.
d.
)° and mPNM = 62°.
mPNO = 40° and mMNO = 22°
mPNO = 22° and mMNO = 40°
mPNO = 16° and mMNO = 46°
mPNO = 46° and mMNO = 16°
____ 12. In the figure (not drawn to scale),
bisects
°, and
°. Solve for x and find
a. 3, 24°
13. If
b. 6, 138°
° and
c. 6, 111°
d. 3, 27°
°, then what is the measure of
?
14.
Name a pair of vertical angles in the figure above.
____ 15. Which figure below is not a polygon?
a.
b.
c.
d.
____ 16. The figure shown
a. is a pentagon
b. is a hexagon
____ 17. Which figure below is not a regular polygon?
a.
b.
c. is a heptagon
d. is a quadrilateral
c.
d.
____ 18. In the figure,
are _____________.
a. alternate interior angles
b. consecutive interior angles
c. alternate exterior angles
d. corresponding angles
____ 19. Find the value of x that will allow you to prove that
below is
parallel to
if the measure of
is
° and the measure of
is 81°. (The figure may not be drawn to scale.)
a. 22
b. 69
c. 23
d. 36
a
1
2
9 10
3 4
b
11 12
5
6
7
8
13 14
15 16
c
20. Which lines, if any, must
given diagram and
justification for each
____ 21. Find the value of x:
a. 127° b. 35° c. 88° d. 145°
____ 22. Find the value of x.
be parallel based on the
information. Give the
conclusion.
d
a.
° b.
° c.
____ 24.
____
° d. 23.
° Given:
to show
a.
and
b.
. What other piece of information is needed
by ASA Congruence Postulate?
c.
d.
=
. Name the theorem or postulate that justifies the
congruence.
a. ASA b. AAS c. SAS d. HL
25. Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair
of triangles is congruent?
26. Open-ended: State one additional fact that is needed for the pair of triangles to
be congruent. Identify the postulate or theorem you would then use to prove
the congruence.
27. Use information in the figure to find
mD.
28. Refer to the figure at right
Find the value of x.
Given:

____ 29. A median of
a.
b.
____ 30. An altitude of
a.
b.
____ 31.
, ABE  EBC
is ____.
c.
is ____.
c.
d.
d.
is an altitude of
. Therefore,
is ______.
a. right
c. isosceles
b. equilateral
d. acute
____ 32. Which side lengths allow you to construct a triangle?
a.
c.
b.
d.
33. Identify the largest angle of
.
C
9
34. True or false:
Triangle CDE is similar to triangle FGH.
35. Given:
. Find the length of
A
10
11
B
.
36. Tell whether the pair of triangles is similar. Explain your
reasoning.
37. Find AC.
____ 38. Based on the pattern, what are the next two terms of the sequence?
5
7
−2, − , −3, − , …
2
2
____ 39. What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
a. If a point is in the first quadrant, then its coordinates are positive.
b. If a point is not in the first quadrant, then the coordinates of the point are not positive.
c. If the coordinates of a point are positive, then the point is in the first quadrant.
d. If the coordinates of a point are not positive, then the point is not in the first quadrant.
____ 40. What is the converse and the truth value of the converse of the following conditional?
If an angle is a right angle, then its measure is 90.
a. If an angle is not a right angle, then its measure is 90. False
b. If an angle is not a right angle, then its measure is not 90. True
c. If an angle has measure 90, then it is a right angle. False
d. If an angle has measure 90, then it is a right angle. True
____ 41. If
find the values of x, EF, and FG. The drawing is not to scale.
a. x = 10, EF = 8, FG = 15
b. x = 3, EF = –6, FG = –6
E
F
at right.
A
c.
d.
|
b.
G
D
E
|
a.
x = 10, EF = 32, FG = 45
x = 3, EF = 8, FG = 15
)
____ 42. Name a median for
c.
d.
)
C
F B
D
____ 43. Find the length of
, given that
triangle and AC = 26.
a. 13
b. 26
is a median of the
c. 52
d. not enough
information
A
____ 44.
B
C
____ 45. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?
a.
c.
b.
d.
____46.Solve for x if m∠RST = 90.
____ 47. Find
a. the length of the radius of circle C and
b. The coordinates of point A, given that ̅̅̅̅
𝐴𝐵 is a diameter of
C (2,3)
B (4,-1)
the circle ?
______ 48.
length.
____
49.
____
50.
____
51.
Line l bisects the segment. Find the indicated
Find AC if AB  2 x  18 and
AC  32  6 x
If ̅̅̅̅
𝐴𝐵 .is an altitude of ∆ABC, what kind of triangle is ∆ABC?
____
52.
Find the value of x.
Then classify the triangle by its angles.
____
53.
ABC  _FGH_.
Corresponding angles A  _____, B  _____, C  _____
Corresponding sides AB  ____, BC  ____, CA  _____
____
54.
Use the similarity statement to find the scale factor of the triangle
on the left to the triangle on the right.
ΔLMN ~ ΔPQR
̅̅̅̅ , with 𝐴(−2,1)𝑎𝑛𝑑 𝐶(4, −3).
55. What is the distance from point 𝐾(3,8) to the midpoint of 𝐴𝐶
J
w-6
56. Find the value of w, x, and y that will make JKLMN a regular polygon.
x+2
K
N
2x
M
y+1
x2
L
57.
A drawer contains 4 white socks, 3 blue socks, and 5 yellow socks. You randomly
choose a sock, put it on, and then randomly choose another. What is the probability that you chose
two blue socks?
58.
A coach needs to select 6 starters from a team of 13 players. In how many ways can these
players be selected?
59. A company needs to choose a president, vice-president, and a mascot from a group of 24
people. In how many ways can the positions be filled?
60. According to the data shown, if an animal is randomly
selected, what is the probability that the animal is a cat or a
female?
61. Give an example of the transitive property.
Cats
Dogs
Total
Males Females Total
12
15
27
11
8
19
23
23
46