Download Geometry CST Std 2-3-22 Multiple Choice Identify the choice that

Geometry CST Std 2-3-22
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Drawings are very helpful when writing a proof.
Which of the following can be assumed from a
a.
. b. M bisects
diagram?
noncollinear with A and B. d.
a. right angles b. supplemental angles c. parallel
lines d. congruent segments
. c. M is
.
3. Another name for a proof using contradiction is:
a. indirect proof b. inductive reasoning
2. Segment
has a midpoint, M. What conclusion
c. paragraph proof d. two-column proof
can you draw?
4. Sean is trying to prove the theorem below using proof by contradiction. Using the diagram below, he assumes that
is not congruent to . Which theorem will Sean use to reach a contradiction?
Theorem: Vertical angles are congruent.
2
3
1
4
a. All right angles are congruent. b. If two angles are supplementary to the same angle, then they are congruent.
c. The sum of supplementary angles sum is 180º. d. If two angles are supplementary and congruent, then they are
right angles.
5. Use the proof to answer the question below.
measure 90º. c. Substitution d. Supplementary
angles are congruent.
Given:
are right angles.
Prove:
6. When using proof by contradiction, what is the first
step?
Statements
Reason
a. Assume what you are trying to prove is true.
s
b. Assume what you are trying to prove is false.
1.
are right angles.
1. Given
c. Use the given information to complete a proof.
2. m
= 90º
2.
d. Assume no given statements are true.
Definition of right angle.
3. m
= 90º
3.
7. Which of the following is not a type of proof?
Definition of right angle.
4.
4. ?
a. Paragraph b. Two-column c. Indirect
d. Conditional
What reason can be used to prove the angles are
congruent?
8. Use the proof to answer the question below.
a. Definition of right angle. b. All right angles
Given:
Prove:
12. Point A has coordinates of (–3, 2). What conclusion
can you draw?
D
F
1
A
2
a. Point A is in Quadrant II. b. Point A is on the xaxis. c. Point A is in Quadrant III. d. Point A is
not in a quadrant.
3
B
C
13. What is the converse of the statement: “If two
angles are vertical angles, then they are
congruent.”
Statements
Reasons
1.
2.
Addition Property of Equality
3.
Addition Property of Equality
4.
Substitution
5.
Reflexive Property
6.
1. Given
2.
3.
4.
14. If a conditional statement is true, which of the
following statements must also be true?
5.
6. ?
a. inverse b. converse c. contrapositive
d. biconditional
a. Substitution Property of Equality b. CPCTC
c. Subtraction Property of Equality d. Addition
Property of Equality
15. “If two angles are right angles, then they are
congruent.”
9. The Reflexive Property can be used to prove which
of these statements?
a.
d.
b.
are right angles.
a. Vertical angles are congruent. b. If two angles
are congruent, then they are vertical angles. c. If
two angles are not vertical angles, then they are
congruent. d. If two angles are not vertical angles,
then they are not congruent.
The validity of the converse of this statement is:
a. true b. false c. cannot be determined d. There
is no converse.
c.
16. Which figure can serve as a counterexample to the
conjecture below.
10. Which shows an example of the Symmetric
Property?
Conjecture: Every triangle has two congruent sides.
a. If
then
then
then
, then
. c. If
. d. If
.
. b. If
, and
, and
11. “Two planes intersect in exactly one line.”
Which of the following would best serve as a
counterexample to the conjecture above?
a. intersecting planes b. perpendicular planes
c. parallel planes d. coplanar lines
,
,
,
a. isosceles triangle b. equilateral triangle
c. scalene triangle d. isosceles right triangle
17. What is the inverse of the statement: “If two angles
are right angles, then the angles are
supplementary.”
a. If two angles are not right angles, then they are
not supplementary. b. If two angles are
supplementary, then they are right angles. c. If two
angles are right angles, then they are not
supplementary. d. If two angles are not
supplementary, then they are not right angles.
18. Which of the following is an example of a true
conditional statement?
a. If two triangle are right triangles, then the
triangles are congruent. b. If a figure has 4 sides,
then it is a parallelogram. c. If an angle is obtuse,
then it has a measurement less than 90º. d. If a
figure is a square, then it is a rectangle.
23. What is the reflection of the point (5, 8) over the
line y = x?
a. (–5, –8) b. (–8, –5) c. (8, 5) d. (5, 5)
24. If triangle XYZ is rotated 90º closewise about the
origin, what are the coordinates of ?
y
19. Sandy’s friend Oliver told her, “If I am wet, then it
is raining outside.” Sandy does not believe his
statement is always true. Which of the following
statements could she not use as a counterexample?
a. Oliver forgot his umbrella and got caught in the
rain. b. Oliver just finished swimming. c. Oliver
just took a shower. d. Oliver was water skiing.
5
4
Z
3
X
2
1
–5
–4
–3
–2
–1
–1
1
–2
20. “If three points are collinear, then they form a
triangle.”
2
3
4
5
x
Y
–3
–4
–5
Which of the following is the contrapositive of the
conjecture?
a. (2, –3) b. (–2, 3) c. (–2, –3) d. (–3, –2)
a. If three points do not form a triangle, then they
are noncollinear. b. If three points are
noncollinear, then they do not form a triangle. c. If
three points do not form a triangle, then they are not
noncollinear. d. If three points form a triangle,
then they are collinear.
21. The vertices of
are X(5, 4), Y(1, –3), and Z(–
2, 2).
is translated 2 units down and 2 units
to the right. What are the new coordinates for the
vertices of the triangle?
25. Regular pentagon FGHJK is shown below. What
point represents a 144º clockwise rotation of point
G about point Y?
F
K
G
a. X(7, 2), Y(3, –5), Z(0, 0) b. X(7, 6), Y(3, –1), Z(–
4, 4) c. X(3, 2), Y(3, –5), Z(0, 4) d. X(3, 2), Y(3, –
1), Z(–4, 4)
22. Sean has a piece of paper with a word written on it.
He cannot read the word unless he holds it up to a
mirror and reads the word in the mirror. Which of
the following describes the transformation that
allows Sean to read the word?
a. reflection b. rotation c. tessellation
d. translation
Y
J
a. F b. H c. J d. K
H
26. The diagram below shows a translation of the solid image to the dotted image. Which rule describes the
translation?
y
9
8
7
6
5
4
3
2
1
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 x
–2
–3
–4
a. (x + 3, y + 3) b. (x + 7, y + 3) c. (x – 7, y – 3) d. (x – 3, y – 7)
27.
Alli needs to rotate a figure 180º about the origin. The coordinates of one of the points is (x, y). Which of
the following represents the coordinates of the point after the rotation?
a. (y, x) b. (–x, –y) c. (–x, y) d. (x, –y)
28. Which of the following figures does not have a line of symmetry?
a.
b.
c.
d.
29. Which of the following describes the transformation shown?
a. translation b. rotation c. reflection d. symmetry
30. Maureen hung a picture on the wall. It was 4 feet from the floor. She moved the picture right 1 foot and up 2 feet.
How high is the picture from the floor?
a. 4 ft b. 5 ft
c. 6 ft d. 7 ft