25 POINTS!
1)
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
2)
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.
