Question

part b
consider the proof ( p parallel q ) given ( \triangle lhk sim \triangle ljz ). if ( \triangle lhk sim \triangle ljz ), then ( angle lhk cong angle ljz ) because corresponding angles in similar triangles are
which statement concludes the proof?
a. if ( angle lhk cong angle ljz ), then ( p parallel q ) because when base angles are congruent, the lines are parallel.
b. if ( angle lhk cong angle ljz ), then ( p parallel q ) because when corresponding angles are congruent, the lines are parallel.
c. if ( angle lhk cong angle ljz ), then ( p parallel q ) because when alternate exterior angles are congruent, the lines are parallel.
d. if ( angle lhk cong angle ljz ), then ( p parallel q ) because when corresponding angles are congruent, the lines are parallel.

Explanation:

• Option A: The concept of "base angles" is not relevant in the context of proving parallel lines using angle - congruence. This option is incorrect.
• Option B: This option is a correct statement. When two lines are cut by a transversal and the corresponding angles are congruent, the two lines are parallel. Here, \(\angle LHK\) and \(\angle LJZ\) are corresponding angles with respect to lines \(p\) and \(q\) and the transversal \(LJ\) (or \(LH\)).
• Option C: \(\angle LHK\) and \(\angle LJZ\) are not alternate exterior angles. Alternate exterior angles are on opposite sides of the transversal and outside the two lines. So, this option is incorrect.
• Option D: This is a repetition of Option B.

Answer:

B. If \(\angle LHK\cong\angle LJZ\), then \(p\parallel q\) because when corresponding angles are congruent, the lines are parallel.