Question

8
choose the options that best fit the blank boxes. (1 point)
1 angle n=angle q
2 mp=mp
3 mn=qp and mq=np
4 sss congruence postulate
5 cpctc

Explanation:

Step1: Recall parallelogram property

In parallelogram \(MNQP\), opposite sides are congruent. So the statement for the first - blank (corresponding to the reason "The opposite sides of a parallelogram are congruent") should be \(MN = QP\) and \(MQ=NP\).

Step2: Recall reflexive property

The reflexive property of congruence states that a segment is congruent to itself. So the statement for the second - blank (corresponding to the reason "Reflexive Property of Congruence") is \(MP = MP\).

Step3: Identify congruence postulate

We have two pairs of congruent sides (\(MN = QP\), \(MQ = NP\)) and a common side (\(MP = MP\)). The postulate used to prove \(\triangle MQP\cong\triangle PNM\) is the SSS (Side - Side - Side) Congruence Postulate.

Step4: Use CPCTC

Once we have proved that \(\triangle MQP\cong\triangle PNM\) by SSS, to prove \(\angle N\cong\angle Q\) we use the Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

Answer:

1. \(MN = QP\) and \(MQ = NP\)
2. \(MP = MP\)
3. SSS Congruence Postulate
4. \(\angle N\cong\angle Q\) (by CPCTC)