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Amanda and Stephen 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

Amanda's Proof

Statement Justification
∠1 + ∠4 = 180° Definition of Supplementary Angles
∠3 + ∠4 = 180° Definition of Supplementary Angles
∠1 + ∠4 = ∠3 + ∠4 Transitive Property of Equality
∠1 ≅ ∠3 Subtraction Property of Equality
Stephen's Proof

Statement Justification
∠1 + ∠2 = 180° Definition of Supplementary Angles
∠2 + ∠3 = 180° Definition of Supplementary Angles
∠1 + ∠2 = ∠2 + ∠3 Transitive Property of Equality
∠1 ≅ ∠3 Subtraction Property of Equality
(5 points)

Stephen is correct, but Amanda is not.
Amanda is correct, but Stephen is not.
Both Amanda and Stephen are correct.
Neither Amanda nor Stephen is correct.
2.
(03.01 MC)
The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ. :

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

According to the given information, segment UV is parallel to segment WZ while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are corresponding angles, they are congruent according to the Corresponding Angles Postulate. Finally, angle VQT is congruent to angle WRS by the _____________________.

Which Property of Equality accurately completes the proof? (5 points)


Reflexive
Substitution
Subtraction
Transitive
3.
(03.01 MC)
The following is an incorrect flowchart proving that point L, lying on line LM which is a perpendicular bisector of segment JK , is equidistant from points J and K:

Segment JK intersects line LM at point N

Line LM is a perpendicular bisector of segment JK, Given. Two arrows are drawn from this statement to the following two stateme

What is the error in this flowchart? (5 points)


JL and KL are equal in length, according to the definition of a midpoint.
An arrow is missing between ∠LNK = 90° and ∠LNJ = 90° and ∠LNK ≅ ∠LNJ.
An arrow is missing between the given statement and ∠LNK ≅ ∠LNJ.
Triangles JNL and KNL are congruent by the Angle-Angle Side (AAS) Postulate.
4.
(03.01 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

When written in the correct order, the two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:

Statements Reasons
segment UV is parallel to segment WZ Given
Points S, Q, R, and T all lie on the same line. Given
I m∠SQT = 180° Definition of a Straight Angle
II m∠SQV + m∠VQT = 180° Substitution Property of Equality
III m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality
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
Which is the most logical order of statements and reasons I, II, and III to complete the proof? (5 points)


I, III, II
II, I, III
II, III, I
III, I, II