Question

What is the answer to this problem

Answer 1

When two pentagons are congruent, then the corresponding angles and sides are equal (congruent).

As, Pentagon
`GDXLP\cong` Pentagon
`ARKMV`

Being congruent, the corresponding sides are equal(congruent).

So,
`\overline{GD} \cong \overline{AR}` ,
`\overline{DX} \cong \overline{RK}` ,
`\overline{XL} \cong \overline{KM}` ,
`\overline{LP} \cong \overline{MV}` ,
`\overline{GP} \cong \overline{AV}` ,
`\overline{GL} \cong \overline{AM}` ,
`\overline{DL} \cong \overline{RM}` ,
`\overline{DP} \cong \overline{RV}` and
`\overline{XP} \cong \overline{KV}`

Being Congruent, corresponding angles are also equal (congruent).

So,
`\angle G \cong \angle A` ,
`\angle D \cong \angle R` ,
`\angle X \cong \angle K` ,
`\angle L \cong \angle M` ,
`\angle P \cong \angle V`

Therefore, Option 2 , 4 and 5 are correct.

That is,
`\angle X \cong \angle K`

`\overline{GP} \cong \overline{AV}`

and
`\overline{PL} \cong \overline{VM}`