Question 1(Multiple Choice Worth 1 points)

(01.07 MC)

Use the figure to answer the question that follows:

segments UV and WZ are parallel with line ST intersecting both at points Q and R, respectively

The two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:


Step Statements Reasons
1 segment UV is parallel to segment WZ Given
2 Points S, Q, R, and T all lie on the same line. Given
3 m∠SQT = 180° Definition of a Straight Angle
4 m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
5 m∠SQV + m∠VQT = 180° Substitution Property of Equality
6 m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
7 Substitution Property of Equality
8 m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRS Subtraction Property of Equality
∠SQV ≅ ∠ZRS Definition of Congruency


What is the missing statement for step 7?
m∠SQV + m∠VQT = 180°
m∠VQT + m∠ZRS = 180°
m∠SQV + m∠VQT = m∠VQT + m∠ZRS
m∠SQV + m∠SQT = 180°
Question 2(Multiple Choice Worth 1 points)

(01.07 MC)

Kelly and Daniel wrote the following proofs to prove that vertical angles are congruent. Who is correct?

Line segment NT intersects line segment MR, forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles.

Kelly's Proof


Statement Justification
∠2 = ∠4 Vertical angles are congruent.
∠1 = ∠3 Vertical angles are congruent.
Vertical angles are congruent. Vertical Angle Theorem

Daniel's Proof

Statement Justification
∠1 + ∠2 = 180° Definition of Supplementary Angles
∠1 + ∠4 = 180° Definition of Supplementary Angles
∠1 + ∠2 = ∠1 + ∠4 Transitive Property of Equality
∠2 = ∠4 Subtraction Property of Equality
Both Kelly and Daniel are correct.
Neither Kelly nor Daniel is correct.
Kelly is correct, but Daniel is not.
Daniel is correct, but Kelly is not.
Question 3(Multiple Choice Worth 1 points)

(01.07 MC)

Use the figure and flowchart proof to answer the question:

Segments UV and WZ are parallel segments that intersect line ST at points Q and R, respectively

Points S, Q, R, and T all lie on the same line; Given. Arrows are drawn from this statement to the following three statements. Statement 1: The measure of angle SQT equals 180 degrees; Reason 1: Definition of a Straight Angle. Statement 2: The measure of angle SQV plus the measure of angle VQT equals the measure of angle SQT; Reason 2: Angle Addition Postulate. Statement 3: The measure of angle SQV plus the measure of angle VQT equals 180 degrees; Reason 3: Substitution Property of Equality. Lines UV and WZ are parallel; Given. An arrow is drawn from this statement to the following statements. Statement 4: The measure of angle VQT plus the measure of angle ZRS equals 180 degrees; Reason A. Statement 5: The measure of angle SQV plus the measure of angle VQT equals the measure of angle VQT plus the measure of angle ZRS; Reason B. An arrow also points from Statement 3 to Statement 5. An arrow from Statement 5 points to the following statements. Statement 6: The measure of angle SQV plus the measure of angle VQT minus the measure of angle VQT equals the measure of angle VQT plus the measure of angle ZRS minus the measure of angle VQT, the measure of angle SQV equals the measure of angle ZRS; Reason C. Statement 7: The measure of angle SQV is congruent to the measure of angle ZRS; Definition of Congruency.

Which theorem accurately completes Reason A?

Alternate Interior Angles Theorem
Corresponding Angles Theorem
Alternate Exterior Angles Theorem
Same-Side Interior Angles Theorem
Question 4(Multiple Choice Worth 1 points)

(01.07 MC)

The figure shown has two parallel lines cut by a transversal:

A pair of parallel lines is shown, crossed by a transversal. Angles are identified as 1, 2, 3, 4, 5, 6, 7, and 8. Angles 1-4 are on the top line clockwise from upper left. Angles 5-8 are on the lower line clockwise from upper left.

Which angle is an alternate interior angle to ∠3?

∠2
∠6
∠5
∠8
Question 5(Multiple Choice Worth 1 points)

(01.07 MC)

Two friends are sharing one half of a pizza that is divided into three pieces, as shown in the figure.

Circle O has diameter A D and radii B O and C O. Angle A O B is adjacent to angle B O C. Angle B O C is adjacent to angle C O D.

If m∠AOB = (3x − 6)° and m∠BOD = (5x + 14)°, what is the value of x?

10.0
21.5
58.5
121.5