Question

1. complete each statement for parallelogram mnpl.

a. (overline{mn}cong)___ and (overline{ml}cong)___
b. (angle nmlcongangle)___ and (angle mlpcongangle)___
c. (overline{mn}parallel)___ and (overline{ml}parallel)___
d. (overline{mr}cong)___ and (overline{lr}cong)___

Explanation:

Step1: Properties of parallelogram (opposite sides)

In a parallelogram, opposite sides are congruent. So, $\overline{MN}\cong\overline{LP}$ and $\overline{ML}\cong\overline{NP}$.

Step2: Properties of parallelogram (opposite angles)

In a parallelogram, opposite angles are congruent. So, $\angle NML\cong\angle NPL$ and $\angle MLP\cong\angle MNP$.

Step3: Properties of parallelogram (opposite sides parallel)

In a parallelogram, opposite sides are parallel. So, $\overline{MN}\parallel\overline{LP}$ and $\overline{ML}\parallel\overline{NP}$.

Step4: Properties of parallelogram (diagonals bisect each other)

In a parallelogram, diagonals bisect each other. So, $\overline{MR}\cong\overline{RP}$ and $\overline{LR}\cong\overline{RN}$.

Answer:

a. $\overline{MN}\cong\overline{LP}$ and $\overline{ML}\cong\overline{NP}$
b. $\angle NML\cong\angle NPL$ and $\angle MLP\cong\angle MNP$
c. $\overline{MN}\parallel\overline{LP}$ and $\overline{ML}\parallel\overline{NP}$
d. $\overline{MR}\cong\overline{RP}$ and $\overline{LR}\cong\overline{RN}$