Download SpringBoard Geometry Unit 1 Part A

Name: ________________________ Class: ___________________ Date: __________
SpringBoard Geometry Unit 1 Part A
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which figure shows that ∠ABC and ∠DBC are supplementary?
A.
C.
B.
D.
1
ID: A
Name: ________________________
____
2. Which of the following angles appears to be obtuse?
A. ∠PQM
B. ∠LVT
____
ID: A
C. ∠RUS
D. ∠MLN
3. Which statement represents a postulate?
I) A line segment can be extended infinitely in a straight line.
II) Complementary angles are two angles with measures that total 90º.
III) Two angles that are supplementary to the same angle are congruent.
IV) If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other
line.
A. I
B. I
____
C. III
D. IV
4. Line can be classified as which of the following?
A. a conjecture
B. an undefined term
C. a definition
D. a theorem
2
Name: ________________________
____
ID: A
5. James designs bicycle wheels, like the one pictured.
He describes the spoke of the wheel as a rod from the center of the wheel to the rim. Which term
can be used for a spoke of the bicycle wheel?
A. chord
B. diameter
____
C. line
D. radius
6. Consider circle A, where AB⊥CD.
Based on the given information, what statement can be made?
A. AB ≅ CD
B. AF ≅ CF
____
C. ∠AFC is a right angle.
1
D. BF = AF
2
7. Jane’s teacher describes MN as a chord of a circle that contains the center of that circle. Jane
states that MN is a diameter of that circle.
What is Jane using to justify her reasoning?
A. conjecture
B. definition
C. postulate
D. theorem
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Name: ________________________
____
ID: A
8. What statement must be true about circle P?
A. The length of MN is greater than the
C. The length of PR is half the length of
length of TS.
TS.
B. The length of PS is the same as the
D. The length of SN is the same as the
length of MN.
____
length of PT .
9. Which of the following statements can be written as a biconditional statement?
A. If a figure is a chord, then it is a line
segment.
B. If two lines are parallel, then the lines
are coplanar and never intersect.
C. If a figure is a square, then it has four
congruent sides.
D. If the measure of an angle is 132º,
then it is obtuse.
____ 10. Which is a counterexample to the conditional statement shown.
If a geometric figure has an endpoint, then it is a line segment.
A. a circle
B. a line
C. a plane
D. a ray
____ 11. Which of the following conditional statements has a false inverse statement?
A. If a quadrilateral is a square, then it
C. If two angles are complementary, then
has four 90º angles.
the sum of their measures is 90º.
B. If two coplanar lines are parallel, then D. If two segments are congruent, then
the alternate interior angles created
the lengths of the segments are equal.
by a transversal are congruent.
4
Name: ________________________
ID: A
____ 12. Consider the diagram shown.
Which definition or postulate justifies the statement m∠RVP = m∠RVU+ m∠UVP?
A. Definition of supplementary angles
B. Definition of complementary angles
C. Angle Addition Postulate
D. Linear Pair Postulate
____ 13. What is the midpoint of ST shown on the grid?
A. (4, 8)
B. (8, 4)
C. (8, 6)
D. (8, 16)
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Name: ________________________
ID: A
____ 14. Mr. Diaz’s class is solving the problem shown.
Given the points A(-2, -1), B(6, 5), and D(-4, 2), what must be the y-coordinate of point E if its
x-coordinate is 2 and AB ≅ DE?
Susan states that the y-coordinate can only be -6.
Julie states that the y-coordinate can only be 10.
Todd states that the y-coordinate can either be 6 or -10.
Courtney states that the y-coordinate can either be -6 or 10.
Which student is correct?
A. Susan
B. Julie
C. Todd
D. Courtney
____ 15. Four students used the diagram shown to determine the value of x.
Which student’s reasoning is correct?
A. Jacob states that the two given angles are complementary; therefore,
1
(5x + 25) + (2x + 43) = 90, so x = 3 .
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B. Carla states that the two given angles are vertical; therefore, (5x + 25) = (2x + 43),
so x = 6.
C. Ferris states that the two given angles are vertical; therefore,
1
(5x + 25) = (2x + 43), so x = 61.
2
D. Elsa states that the two given angles are supplementary; therefore,
(5x + 25) + (2x + 43) = 180, so x = 16.
6
Name: ________________________
ID: A
____ 16. Sarah provides the two-column proof shown.
Given: ∠3 ≅ ∠6
Prove: r Ä s
Statements
1. ∠3 ≅ ∠6
2. m∠3 = m∠6
3. ∠3 and ∠4 are a linear pair.
4. ∠3 and ∠4 are supplementary.
5. m∠3 + m∠4 = 180°
6. m∠6 + m∠4 = 180°
7. ∠6 and ∠4 are supplementary.
8. r Ä s
Reasons
1. Given
2. Definition of congruent angles
3. Definition of a linear pair
4. Linear Pair Postulate
5. Definition of supplementary angles
6. Transitive Property of Equality
7. Definition of supplementary angles
8. ______________________
What is the missing reason?
A. Converse of Alternate Interior Angles
Theorem
B. Same-Side Interior Angles Theorem
C. Linear Pair Postulate
D. Converse of Same-Side Interior
Angles Postulate
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Name: ________________________
ID: A
____ 17. In the diagram shown, the path from the swings to the slide is the perpendicular bisector of the path
from the merry-go-round to the sandbox.
Which of the following can be proven from the given information?
I. The distance from the sandbox to the merry-go round is 36 ft.
II. The two paths form a 90° angle where they intersect at the slide.
A.
B.
C.
D.
I only
II only
Both I and II
Neither I nor II
____ 18. The line segments in this diagram represent the four walking paths that the town of Math designed to
pass a memorial located in the triangular center.
The mayor would like to place park benches within congruent angles. Which of the following angle
pairs can be chosen?
A. ∠AEF and ∠GEB
B. ∠AEJ and ∠CJH
C. ∠EKJ and ∠DKI
D. ∠KEB and ∠JKE
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Name: ________________________
ID: A
____ 19. A teacher provides a diagram of parallel lines cut by a transversal.
Which angle pair is congruent, given d Ä f?
A. ∠4 and ∠1
B. ∠3 and ∠7
____ 20. Which can be used to show that
C. ∠6 and ∠7
D. ∠4 and ∠5
RSQ is a right triangle?
A. The slope of RS is 2 and the slope of
1
SQ is .
2
C. The slope of SQ is −
B. The slope of RS is 2 and the slope of
1
SQ is − .
2
D. The slope of SQ is
of RQ is
RQ is
9
1
.
3
1
and the slope
2
1
.
3
1
and the slope of
3
Name: ________________________
ID: A
____ 21. Which equation represents a line perpendicular to the line shown on the graph?
A. −15x + 6y = 90
B. −8x + 20y = −60
C. 2x + 5y = −15
D. 10x + 4y = −38
____ 22. Determine an equation of the line that passes through (3, -4) and is parallel to the line −2x + 3y = −15.
A. y = −2x + 2
3
1
B. y = − x +
2
2
2
x−6
3
2
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D. y = x +
3
3
C. y =
10