Question

1. select the reasons that justify the statements in the proof table: given: ( mq parallel np ) prove: ( \triangle qmo sim \triangle pno )

Explanation:

Step1: Given condition

The statement \(MQ\parallel NP\) is given in the problem, so the reason A is "Given".

Step2: Corresponding angles

Since \(MQ\parallel NP\), when a transversal \(OQ\) intersects them, \(\angle OPN\) and \(\angle OQM\) are corresponding angles. By the Corresponding Angles Postulate, \(\angle OPN\cong\angle OQM\), so the reason B is "Corresponding Angles Postulate".

Step3: Reflexive property

\(\angle O\cong\angle O\) because any angle is congruent to itself. This is the Reflexive Property of Congruence, so the reason C is "Reflexive Property of Congruence".

Step4: AA similarity criterion

We have two pairs of congruent angles (\(\angle OPN\cong\angle OQM\) and \(\angle O\cong\angle O\)). By the AA (Angle - Angle) Similarity Postulate, \(\triangle QMO\sim\triangle PNO\). So the reason D is "AA Similarity Postulate".

Answer:

A. Given; B. Corresponding Angles Postulate; C. Reflexive Property of Congruence; D. AA Similarity Postulate.