Download Geometry Fall 2016 Review for Midterm

Geometry Midterm Review Questions (Questions 1-12) at the end
13. m  ABD  m  DBE  m  EBG  180 This equation is an example of:
a. Segment addition postulate
b. Angle addition postulate
c. Addition property of equality
d. None of the above
D
A
F
E
B
C
G
14. The difference between the measure of the supplement and the measure of the complement of an angle is the
measure of
a. An acute angle
b. A right angle
c. An obtuse angle
d. A straight angle
15. If  C is the complement of  A , and  S is the supplement of  A , which statement is always true?
a. 𝑚 < 𝐶 + 𝑚 < 𝑆 = 180°
b. 𝑚 < 𝐶 > 𝑚 < 𝑆
c. 𝑚 < 𝐶 < 𝑚 < 𝑆
d. 𝑚 < 𝐶 + 𝑚 < 𝑆 = 90°
16. If the measure of angle exceeds the measure of its complement by 20°, the measure of the angle is
a. 100°
b. 35°
c. 55°
d. 105°
17. If two angles have a common vertex, they are ___________ adjacent angles.
a. Sometimes
b. Always
c. Never
18. Given the statement: “If two lines are cut by a transversal so that the corresponding angles are congruent, then the
lines are parallel.”
What is true about the statement and its converse?
a. The statement and its converse are both true.
b. The statement is false, but its converse is true.
c. The statement and its converse are both false.
d. The statement is true, but its converse is false.
19. Which statement is logically equivalent to “If the team has a good pitcher, then the team does not have a good
season”?
a) If the team does not have a good season, then
the team has a good pitcher.
b) If the team does have a good pitcher, then the
team does not have a good season.
c)
If the team has a good season, then the team
does not have a good pitcher.
d) The team has a good pitcher and the team does
not have a good season.
20. In the diagram of ABC and DEF below, AB ≅ DE, ∠A ≅ ∠D, and ∠B ≅ ∠E.
Which method can be used to prove ABC ≅ DEF?
a.
b.
c.
d.
Side angle side congruence
Side side side congruence
Angle side angle congruence
Hypotenuse-leg theorem
21. In the diagram of
below,
triangle, such that
What is
and
. Line segment MS connects points M and S on the
.
?
a) 163
b) 121
c)
42
d) 17
22. In
,
,
, and
. Which statement is true?
a)
b)
c)
d)
23. Juliann plans on drawing
, where the measure of
can range from 50° to 60° and the measure of
range from 90° to 100°. Given these conditions, what is the correct range of measures possible for
?
a) 20° to 40°
b) 30° to 50°
c)
80° to 90°
d) 120° to 130°
24. In the diagram below,
If
and
is isosceles with
, what is
.
?
a) 27
b) 28
c)
42
d) 70
25. For a triangle, which two points of concurrency could be located outside the triangle?
a) incenter and centroid
b) centroid and orthocenter
c)
incenter and circumcenter
d) circumcenter and orthocenter
26. The degree measures of the angles of
are represented by x, 3x, and
Find the value of x.
27. In right
,
degrees less than twice
and
. Find
.
is 12
.
can
28)
29)
30)
31)
32) In an equilateral triangle, what is the difference between the sum of the exterior angles and the sum of the interior angles?
a) 180°
b) 120°
c)
90°
d) 60°
33)
27.In
, the measure of angle A is
fifteen less than twice the measure of angle B.
The measure of angle C equals the sum of the
measures of angle A and angle B. Determine
the measure of angle B.
34. The diagram below shows
If
, what is
, with
,
, and
.
?
a) 26
b) 38
c)
52
d) 64
35.
In
,
,
, and
. Which type of triangle is
a) right
b) scalene
c)
isosceles
d) equilateral
36.
In
,
,
, and
. What is the value of x?
a) 29
b) 31
c)
59
d) 61
The next two questions refer to diagram 1.
37. Which of the following objects is identical to AB ?
(1)
AB
(2)
BA
(3)
BD
(4)
AC
Answer:
_____
38. Which of the following is an example of an undefined
term?
(1) Line segment
(2) Plane
(3) Ray
(4) Triangle
Diagram 1
?
39. Which of the following statements is true?
I BCF is the same as FCA .
II mBCD  mDCF  mACF
III E, B, and A are coplanar.
(a) I only
(b) I and II only
(c) II and III only
(d) I, II, and III
40. Which of the following could not be true of two planes in space?
(1) They could be parallel and not intersect
(3) They could not intersect and not be parallel
(2) They could intersect in a line
(4) They could be coincident
41. It is impossible for two angles to be both
(1) Corresponding and supplementary
(2) Vertical and Complementary
(3) Complementary and supplementary
(4) Alternate Interior and Supplementary
Answer: _____
42. Consider points A,B, C, and D in space. Assume that the four points do not all lie in a single
plane. Consider the following statements.
I
II
III
A, B, and C must all lie in a single plane
A, B, and D must all lie in a single plane
A, B, and C must all lie on a line
Which of the above statements are true?
(1) I only
(2) I and II only
(3) I and III only
(4) II only
43. In the diagram at right, lines m and n are cut by transversal
t. What value of x would make lines m and n parallel?
(1) x  20
(3)
x  75
Answer: _____
(2) x  55
(4)
x  100
Answer: _____
44. Given lines l , m , and n , suppose we have that l m and m and n intersect in a single point
P. Which of the following statements is not necessarily true?
(1) lines l , m are coplanar
(2) There is no point on both l and m
(3) lines l , n are coplanar
(4) l and n intersect in a single point
45. Line segment AB is shown in the diagram below. Which two sets of construction marks, labeled I, II, III,
and IV, are part of the construction of the perpendicular bisector of line segment AB?
(1)
(2)
(3)
(4)
I and II
I and III
II and III
II and IV
46. The diagram below shows two intersecting circles, a circle with center A and a circle with center B.
What type of triangle is triangle ABC?
a. Isosceles
b. Equilateral
c. Scalene
(1)
(2)
(3)
(4)
a. and b.
a. and c.
a. only
b. only
47. One step in a construction uses the endpoints of segment AB to create arcs with congruent radii from
point A and point B. The two arcs intercept above and below the segment at point C and point D. What
is the relationship between segment AB and segment CD?
a. Collinear
b. Parallel
c. Perpendicular
d. Congruent
48) The diagram below shows the construction of line m, parallel to line , through point P.
Which theorem was used to justify this construction?
(1) If two lines are cut by a transversal and the alternate
interior angles are congruent, the lines are parallel.
(2) If two lines are cut by a transversal and the interior
angles on the same side are supplementary, the lines
are parallel.
(3) If two lines are perpendicular to the same line, they are
parallel.
(4) If two lines are cut by a transversal and the
corresponding angles are congruent, they are parallel.
49) Based on the diagram below, which statement is true?
(1)
(2)
(3)
(4)
50) Angle EFG is a straight angle. Angle EFO and angle OFG are adjacent angles. If EFO = 9x and OFG =
9x2. What is the measure of OFG?
(1)
(2)
(3)
(4)
144o
36o
72o
4o
51) Solve for x and y.
(1)
(2)
(3)
(4)
x = -5, y = 15
x = 5, y = -15
x = 30, y = 5
x = 5, y = -30
52) Choose the word that correctly completes the following postulate:
A line passing through two distinct points in one plane _______ lies completely in that plane.
53.
54.
55.
(1)
always
(2)
sometimes
(3)
never
(4)
this statement is not a postulate
56.
57. Consider the reflection of a point, A, in a line t, and the segment connecting A and its reflection, A’. Which
of the following is not true?
a) A and A’ are equidistant from any point on t.
b) Line t intersects the segment ̅̅̅̅̅
𝐴𝐴′at its midpoint.
̅̅̅̅̅ is the perpendicular bisector of t.
c) Segment 𝐴𝐴′
d) ⃡𝐴𝐴′ is the only line in the plane perpendicular to t.
58. The orthocenter and circumcenter of a triangle are concurrent. What kind of triangle must this triangle be?
a) Equilateral
b) Right
c) Isosceles
d) Acute
59. According to the construction to the right, which of the
following statements must be true?
(I) ̅̅̅ ̅̅̅̅
𝐽𝑂 ≅ 𝐾𝑂
(II)̅̅̅̅ ̅̅̅̅
𝑋𝑂 ≅ 𝑌𝑂
(III) ̅̅̅ ̅̅̅̅
𝑋𝐼 ≅ 𝑋𝐾
(1) Statement I only
(2) Statements I and II only
(3) Statements I and III only
(4) Statements I, II, and III
60. In the diagram at the right, which set of points are
noncoplanar?
(1) A, R, and B
(2) T, S, and B
(3) X, R, and Y
(4) All of these sets of points are coplanar.
61. Which of the following transformations of the plane is not a rigid motion?
(1) Reflection over a line
(2) Rotation about a point
(3) Dilation through a point
(4) Translation
Answer: _____
62. Suppose in ABC , we have AB  AC . Which of the following transformations could be used in a proof by rigid
motion that B  C ?
(1)
(2)
(3)
(4)
Counterclockwise rotation about A by mB
Counterclockwise rotation about B by mA
Reflection over BC
Reflection over the perpendicular bisector of BC
Answer: _____
63. Suppose the plane undergoes a translation T along AB . Suppose m is a line in the plane, and n is the image of m
under the translation T. Suppose also that m  AB . Which of the following statements is true?
(1)
(2)
(3)
(4)
m and n intersect, but are not necessarily perpendicular
mn
m n
Not enough information is given to draw a conclusion
Answer: _____
64. Suppose the plane undergoes a translation T along AB . Suppose m is a line in the plane, and n is the image of m
under the translation T. Which of the following conditions would guarantee that m and n are coincident?
I
m AB
II
A lies on m
III
A and B both lie on m
(1) I only
(2) III only
(3) II and III only
(4) I and III only
Answer: _____
65. Let T be a translation of the plane along AB . Suppose the image of ABC is PQR . Which of the following
statements must be true?
I
AC PR
II
B and P are coincident
III
A, B and P are coincident
(1) I only
(2) III only
(3) I and III only
(4) I, II, and III
Answer: _____
66. What is the smallest angle measure that an equilateral triangle could be rotated about its center and mapped onto
itself?
(1) 30 degrees
(3) 90 degrees
(2) 60 degrees
(4) 120 degrees
Answer: _____
67. In the diagram at right, which rigid motion,
applied to ABC , could be used to show that
ABC is congruent to CQR ?
(1) Reflection over BC
(2) Clockwise rotation about C by mACB
(3) Translation along AC
(4) Reflection over a line m perpendicular to AC at
C
Answer: _____
68. The image of ABC , when reflected about the perpendicular bisector of BC , is CBA . Which of the following
statements must be true?
(1) ABC is equilateral
(2) ABC is isosceles
(3) ABC is right
(4) ABC is scalene
Answer: _____
69) Given the diagram below with four congruent triangles 1, 2, 3, and 4, identify the rigid motion that maps
triangle 2 to triangle 3. Write a congruency statement using the lettered vertices of each triangle.
(1) Translation along segment BY; ∆𝐵𝑍𝑌 ≅ ∆𝑋𝑍𝑌
(2) Translation along segment BY; ∆𝐵𝑍𝑌 ≅ ∆𝑋𝑌𝑍
(3) Reflection over segment ZY; ∆𝐵𝑍𝑌 ≅ ∆𝑋𝑍𝑌
(4) Reflection over segment ZY; ∆𝐵𝑍𝑌 ≅ ∆𝑋𝑌𝑍
70)
71) Consider the diagram at right. Which sequence of
transformations could map ABCD onto HGFE?
(1) rotation then translation
(2) rotation, then translation, then rotation
(3) line reflection, then translation
(4) line reflection, then line reflection
Answer: _____
72) In the diagram at right, ABC  XYC . Which rigid motion
could be used to map ABC onto XYC ?
(1) Reflection over AC
(2) Clockwise rotation about C by 180
(3) Translation along AC
(4) Reflection over the perpendicular bisector of AY
73)
74)
75)
77)
78)
79) Which point below completes the construction of an equilateral triangle?
A) 1
B) 2
C) 3
D)
4
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅ , to complete the
̅̅̅̅, 𝑋𝑌
̅̅̅̅ ≅ 𝐴𝐶
80) Which point is point C of isosceles triangle ABC if you use segment 𝑋𝑌
̅̅̅̅
construction on base 𝐴𝐵 ?
A) 1
B) 2
C) 3
D)
4
D)
4
81) Which point lies on the angle bisector?
A) 1
B) 2
C) 3
82. Which ray will complete the angle so as to be congruent to the angle at left?
A) 𝑄𝑅
B) 𝑄𝑆
C) 𝑄𝑇
D) 𝑄𝑉
̅̅̅̅ ∥ 𝐴𝐷
̅̅̅̅ ; ∠5 ≅ ∠6
Given: 𝐵𝐶
Prove: ∠1 ≅ ∠4
Statement
Reason
̅̅̅̅ ∥ 𝐴𝐷
̅̅̅̅; ∠5 ≅ ∠6
1) 𝐵𝐶
1) Given
2) ∠2 ≅ ∠3
2) _____________________
3) ̅̅̅̅
𝐵𝐷 ≅ ̅̅̅̅
𝐵𝐷
3) Reflexive Property
4) ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐷𝐵
4) AAS Theorem
5) ∠1 ≅ ∠4
5) _____________________
83) Which reason best justifies statement (2) in the proof?
(1) If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
(2) If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.
(3) If two parallel lines are cut by a transversal, then corresponding angles are congruent.
(4) Corresponding parts of congruent triangles are congruent.
84) Which reason best justifies statement (5) in the proof?
(1) If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
(2) If two parallel lines are cut by a transversal, then alternate exterior are congruent.
(3) If two parallel lines are cut by a transversal, then corresponding angles are congruent.
(4) Corresponding parts of congruent triangles are congruent.
85) In the figure below, JL = ML =12, m∠JKL= m∠MKL= 32°, m∠MLK= (24 + 3x)°, and m∠JLK=
From the information given, what must the value of x be?
(1) 3
(2) 6
(3) 8
(4) There is not sufficient information to determine the value.
1. In the diagram at right, which of the following
construction marks are necessary to construct the angle
bisector of the given angle?
(1) III and IV only
(2) I, III and IV only
(3) I, II, and IV only
(4) I, II, III, and IV
2. Point P divides any triangle ABC into 6 triangles of equal area. To
locate point P, what should one construct?
(1)
(2)
(3)
(4)
(5)
Perpendicular bisectors
Centroid
Altitudes
Incenter
Parallel Lines
3. Which is a conditional statement that is logically equivalent to “If the negotiations fail, the baseball
strike will not end.”
(1)
(2)
(3)
(4)
If the negotiations do not fail, the baseball strike will end.
If the baseball strike will not end, then the negotiations fail.
If the baseball strike ends, then the negotiations do not fail.
If the baseball strike ends, then the negotiations succeed.
4. Which set of points are coplanar?
(1) B,S,P
(2) S,V,R
(3) T,V,P
(4) A,R,B
5. Which of the following is an example of a statement that is true and whose converse is true?
(1) If two angles are adjacent, then they share a common vertex.
(2) If two triangles are congruent, then each interior angle of one triangle is congruent to each interior angle of the
other triangle.
(3) If a quadrilateral is equilateral, then the quadrilateral is equiangular.
(4) If a quadrilateral's diagonals bisect each other, the quadrilateral is a parallelogram.
6. In a building, planes W, X, and Y represent each of the three floors; planes Q and R represent the front and back of
the building; planes S and T represent the sides. Which is a true statement?
(1) Planes W and Y intersect in a line.
(2) Planes Q and X intersect in a line.
(3) Planes W, X and T intersect in a point.
(4) Planes Q, R, and S intersect in a point.’
7. Suppose point G represents a duck flying over a lake, points H and J represent two ducks swimming on the lake, and
plane Z represents the lake. Which is a true statement?
(1) There are two lines through G and J.
(2) The line containing G and H lies in plane Z
(3) G, H, and J are noncoplanar.
(4) There is exactly one plane containing points G, H, and J.
̅̅̅̅ ≅ 𝑊𝑋
̅̅̅̅̅
Given: 𝑌𝑋
̅̅̅̅
𝑍𝑋 bisects < 𝑌𝑋𝑊
8. Provide the missing reasons in the
proof shown at right.
Prove: : ̅̅̅̅
𝑌𝑍 ≅ ̅̅̅̅̅
𝑊𝑍
Statement
Reason
1. ̅̅̅̅
𝑌𝑋 ≅ ̅̅̅̅̅
𝑊𝑋
̅̅̅̅
𝑍𝑋 bisects < 𝑌𝑋𝑊
1. Given
2. < 𝑌𝑋𝑍 ≅< 𝑊𝑋𝑍
2.
3. ̅̅̅̅
𝑋𝑍 ≅ ̅̅̅̅
𝑋𝑍
3.
4. ∆𝑌𝑋𝑍 ≅ ∆𝑊𝑋𝑍
4.
̅̅̅̅̅
5. ̅̅̅̅
𝑌𝑍 ≅ 𝑊𝑍
5.
9. At right is triangle JKL with medians LS, RK, and JQ. If LS = 2x + 6
and LW = 2x - 2, then what are LS, LW, and WS?
A
B
W
X
D
C
Z
Y
10. If A maps to Y and B maps to Z, what series of
transformations maps quadrilateral ABCD onto quadrilateral
WXYZ ?
11. Construct a line segment AB and its perpendicular bisector. Let C be the midpoint of AB
Say that AC  x 2  30 and BC  x . What can x be?
Why do you think a student would say that x  5 works?
12. Find the missing angles in the diagram at
right.