Question

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

Explanation:

Step1: Recall parallelogram property

In parallelogram \(MNQP\), opposite - sides are congruent. So, \(MN = QP\) and \(MQ=NP\).

Step2: State reflexive property

\(MP\) is common to both \(\triangle MQP\) and \(\triangle PNM\), so \(MP = MP\) by the reflexive property of congruence.

Step3: Apply SSS congruence

Since \(MN = QP\), \(MQ = NP\), and \(MP = MP\), by the SSS (Side - Side - Side) Congruence Postulate, \(\triangle MQP\cong\triangle PNM\).

Step4: Use CPCTC

Corresponding Parts of Congruent Triangles are Congruent (CPCTC). So, \(\angle N=\angle Q\).

Answer:

1. \(MN = QP\) and \(MQ = NP\) (The opposite sides of a parallelogram are congruent)
2. \(MP = MP\) (Reflexive Property of Congruence)
3. \(\triangle MQP\cong\triangle PNM\), SSS Congruence Postulate
4. \(\angle N=\angle Q\), CPCTC