EDGE Math 8

Identify the missing statement or reason to complete the two-column proof. Type the letter of your answer in the box.

Given:	Quadrilateral QUAD is a parallelogram. $M, N, O,$ and P are midpoints of $\bar{QD},$ $\bar{QU},$ $\bar{UA},$ and $\bar{AD},$ respectively.
Prove:	Quadrilateral MNOP is a parallelogram.

Choices:

a.	$\bar{NO} ≅ \bar{PM}$
b.	$\bar{NP} ≅ \bar{OM}$
c.	CPCTC
d.	$Δ M Q N ≅ Δ O A P$
e.	If two pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

f.	Opposite angles of a parallelogram are congruent.
g.	Opposite sides of a parallelogram are congruent.
h.	$\bar{QN} ≅ \bar{NU} ≅ \bar{AP} ≅ \bar{PD}$
i.	Construction and Line Postulate
j.	$M, N, O,$ and P are midpoints of $\bar{QD},$ $\bar{QU},$ $\bar{UA},$ and $\bar{AD},$ respectively.

Proof:

Statements

Reasons

1. Quadrilateral QUAD is a parallelogram.

1. Given

∠ M Q N ≅ ∠ O A P

∠ N U O ≅ ∠ P D M

\bar{Q U} ≅ \bar{D A}

\bar{Q D} ≅ \bar{U A}

\bar{QM} ≅ \bar{MD} ≅ \bar{AO} ≅ \bar{UO}

4. Definition of midpoint

Δ M D P ≅ Δ O U N

5. SAS Congruence Postulate

\bar{MN} ≅ \bar{OP}

7. Quadrilateral MNOP is a parallelogram.

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