When two pentagons are congruent, then the corresponding angles and sides are equal (congruent).
As, Pentagon [tex] GDXLP\cong [/tex] Pentagon [tex] ARKMV [/tex]
Being congruent, the corresponding sides are equal(congruent).
So, [tex] \overline{GD} \cong \overline{AR} [/tex] , [tex] \overline{DX} \cong \overline{RK} [/tex] , [tex] \overline{XL} \cong \overline{KM} [/tex] , [tex] \overline{LP} \cong \overline{MV} [/tex] , [tex] \overline{GP} \cong \overline{AV} [/tex] , [tex] \overline{GL} \cong \overline{AM} [/tex] , [tex] \overline{DL} \cong \overline{RM} [/tex] , [tex] \overline{DP} \cong \overline{RV} [/tex] and [tex] \overline{XP} \cong \overline{KV} [/tex]
Being Congruent, corresponding angles are also equal (congruent).
So, [tex] \angle G \cong \angle A [/tex] , [tex] \angle D \cong \angle R [/tex] , [tex] \angle X \cong \angle K [/tex] , [tex] \angle L \cong \angle M [/tex] , [tex] \angle P \cong \angle V [/tex]
Therefore, Option 2 , 4 and 5 are correct.
That is,[tex] \angle X \cong \angle K [/tex]
[tex] \overline{GP} \cong \overline{AV} [/tex]
and [tex] \overline{PL} \cong \overline{VM} [/tex]
