Question 1(Multiple Choice Worth 4 points)

Question

(01.07 LC)

Lines BC and ED are parallel. They are intersected by transversal AE, in which point B lies between points A and E. Lines BC and ED are also intersected by transversal EC. Angle ABC measures 70 degrees, and angle CED measures 30 degrees.

What angle relationship describes angles BCE and CED?

Alternate interior angles
Alternate exterior angles
Corresponding angles
Same-side interior angles
Question 2(Multiple Choice Worth 4 points)
(01.06 LC)

line BE, line FC, and ray AD intersecting at A

Angles BAE and FAC are straight angles. What angle relationship best describes angles BAC and DAC?

Adjacent angles
Complementary angles
Supplementary angles
Vertical angles
Question 3(Multiple Choice Worth 4 points)
(01.02 MC)

Ben uses a compass and straightedge to bisect segment PQ, as shown:

segment PQ with compass open to greater than half of segment PQ

Which statement best explains why Ben must open the compass to a width greater than half of segment PQ?

To be able to create two intersecting arcs above and below the line segment
To be able to create arcs above the line segment
To find the length of the line segment
To find the length of half of the line segment
Question 4(Multiple Choice Worth 4 points)
(01.06 MC)

Point A is on line EB between points E and B, and ray AF forms adjacent angles EAF with a measure of 3x and FAB with a measure of 2x.

Solve for x.

x = 5°
x = 18°
x = 30°
x = 36°
Question 5(Multiple Choice Worth 4 points)
(01.02 MC)

Which of the following is the final step in bisecting a line segment?

Keeping the compass at the same width, place the compass on the other endpoint and swing arcs on either side so that they intersect the first two arcs created.
Mark the intersection points of the arcs, and draw a line through those two points.
Place the compass on one of the endpoints, and open the compass to a distance more than halfway across the segment.
Swing an arc on either side of the segment.
Question 6(Multiple Choice Worth 4 points)
(01.05 LC)

Which is a counterexample of the following conditional statement:

"If a number is divisible by 4, then it is divisible by 8."

8
20
24
27
Question 7(Multiple Choice Worth 4 points)
(01.06 MC)

segment AE of length 12 with point M between A and E such that segment AM is marked congruent to segment ME

Kyle is creating a frame for a model car. He begins by piecing two rods together, as shown in the diagram. Justify why AM = 6.

Definition of Perpendicular Bisector
Definition of Midpoint
Addition Property
Subtraction Property
Question 8(Multiple Choice Worth 4 points)
(01.07 MC)

Line AB is parallel to EF. Transversal GJ crosses line AB at K and crosses line EF at L. The measure of angle ELJ is 120 degrees.

Daniel is constructing a fence that consists of parallel sides line AB and line EF. Complete the proof to explain how he can show that m∠GKB = 120° by filling in the missing justifications.

Statement Justification
line AB ∥ line EF
m∠ELJ = 120° Given
m∠ELJ + m∠ELK = 180° Linear Pair Postulate
m∠BKL + m∠GKB = 180° Linear Pair Postulate
m∠ELJ + m∠ELK = m∠BKL + m∠GKB Transitive Property
∠ELK ≅ ∠BKL 1.
m∠ELK = m∠BKL 2.
m∠ELJ + m∠ELK = m∠ELK + m∠GKB Substitution Property
m∠ELJ = m∠GKB Subtraction Property
m∠GKB = m∠ELJ Symmetric Property
m∠GKB = 120° Substitution
1. Alternate Interior Angles Theorem; 2. Definition of Congruence
1. Alternate Exterior Angles Theorem; 2. Substitution Property
1. Definition of Congruence; 2. Alternate Interior Angles Theorem
1. Substitution Property; 2. Alternate Exterior Angles Theorem
Question 9(Multiple Choice Worth 4 points)
(01.07 MC)

Fill in the missing statement and reason in the proof of the corresponding angles theorem.

Segment AB is parallel to segment CD, and transversal EF intersects segment AB at G and segment CD at H.

It is given that segment AB is parallel to segment CD and points E, G, H, and F are collinear. The measure of ∠EGF is 180°, by the definition of a straight angle. ∠AGE and ∠AGF are adjacent, so the measure of ∠AGE plus the measure of ∠AGF equals the measure of ∠EGF, by the Angle Addition Postulate. Then, substituting for the measure of ∠EGF it can be said that the measure of ∠AGE plus the measure of ∠AGF equals 180°. ________, so the measure of ∠CHE plus the measure of ∠AGF equals 180°. Substituting once again means that the measure of ∠AGE plus the measure of ∠AGF equals the measure of ∠CHE plus the measure of ∠AGF. The measure of ∠AGE is equal to the measure of ∠CHE ________. Finally, by the definition of congruence, ∠AGE is congruent to ∠CHE.

∠CHE and ∠AGF are alternate interior angles; using the Transitive Property of Equality
∠CHE and ∠AGF are alternate interior angles; using the Subtraction Property of Equality
∠CHE and ∠AGF are same-side interior angles; using the Subtraction Property of Equality
∠CHE and ∠AGF are same-side interior angles; using the Transitive Property of Equality
Question 10(Multiple Choice Worth 4 points)
(01.05 MC)

What is the converse of the following conditional statement?

"If two angles form a linear pair, then they are supplementary angles."

If two angles are supplementary angles, then they form a linear pair.
If two angles do not form a linear pair, then they are not supplementary angles."
If two angles are not supplementary angles, then they do not form a linear pair.
Two angles form a linear pair if and only if they are supplementary angles.
Question 11(Multiple Choice Worth 4 points)
(01.05 LC)

What is the inverse of the following conditional statement?

"If a number is a prime number, then it has no factors other than one and itself."

If a number is not a prime number, then it has factors other than one and itself.
If a number has no factors other than one and itself, then it is a prime number.
A number is a prime number if and only if it has no factors other than one and itself.
If a number has factors other than one and itself, then it is not a prime number.
Question 12(Multiple Choice Worth 4 points)
(01.05 LC)

What is the contrapositive of the following conditional statement?

"If I won the lottery, then I would buy a car."

If I bought a car, then I won the lottery.
If I did not buy a car, then I did not win the lottery.
If I did not win the lottery, then I would not buy a car.
If I won the lottery, then I would buy a car.
Question 13(Multiple Choice Worth 4 points)
(01.07 MC)

Ray AT bisects ∠MAR. If m∠MAT = (6x − 4)° and m∠RAT = (2x + 8)°, what is the m∠MAR.

62°
28°
14°
3°
Question 14(Multiple Choice Worth 4 points)
(01.07 MC)

Janet is designing a frame for a client. She wants to prove to her client that m∠AGE ≅ m∠CHE in her sketch. What is the missing justification in the proof?

Segment AB is parallel to segment CD, and transversal EF intersects segment AB at G and segment CD at H.

Statement Justification
segment AB is parallel to segment CD with transversal segment EF Given
m∠AGE ≅ m∠HGB Vertical Angles Theorem
m∠HGB ≅ m∠CHE Alternate Interior Angles Theorem
m∠AGE ≅ m∠CHE
Alternate Exterior Angles Theorem
Corresponding Angles Theorem
Reflexive Property
Transitive Property
Question 15(Multiple Choice Worth 4 points)
(01.02 LC)

Which of these is a correct step in constructing congruent line segments?

Use a straightedge to draw two equal arcs from the endpoints.
Use a compass to join the endpoints of the line segment.
Use a straightedge to measure the length of the line segment.
Use a compass to create the distance between the endpoints.

Answer 1

Here are the answers to your multiple-choice questions:

Question 1:
Answer: Alternate interior angles

Question 2:
Answer: Supplementary angles

Question 3:
Answer: To be able to create two intersecting arcs above and below the line segment

Question 4:
Answer: x = 36°

Question 5:
Answer: Mark the intersection points of the arcs, and draw a line through those two points.

Question 6:
Answer: 20

Question 7:
Answer: Definition of Midpoint

Question 8:
Answer: 1. Alternate Interior Angles Theorem; 2. Definition of Congruence

Question 9:
Answer: ∠CHE and ∠AGF are same-side interior angles; using the Transitive Property of Equality

Question 10:
Answer: If two angles are supplementary angles, then they form a linear pair.

Question 11:
Answer: If a number is not a prime number, then it has factors other than one and itself.

Question 12:
Answer: If I did not buy a car, then I did not win the lottery.

Question 13:
Answer: 62°

Question 14:
Answer: Transitive Property

Question 15:
Answer: Use a compass to create the distance between the endpoints.

Feel free to ask if you need further explanations or assistance!