Question

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

Explanation:

Step1: Recall parallelogram properties

In parallelogram \(MNQP\), opposite - angles are equal, so \(\angle N=\angle Q\).

Step2: Identify reflexive property

\(MP = MP\) by the reflexive property of congruence.

Step3: Use side - side - side (SSS) congruence

Since \(MN = QP\) and \(MQ = NP\) (opposite sides of a parallelogram are equal) and \(MP = MP\), by the SSS Congruence Postulate, \(\triangle MQP\cong\triangle PNM\).

Step4: Apply CPCTC

Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

Answer:

1. \(\angle N=\angle Q\) (Opposite angles of a parallelogram are equal)
2. \(MP = MP\) (Reflexive Property of Congruence)
3. \(MN = QP\) and \(MQ = NP\) (Opposite sides of a parallelogram are equal)
4. SSS Congruence Postulate
5. \(\triangle MQP\cong\triangle PNM\)
6. CPCTC