Answer
1) First, prove that $\triangle BAE\cong\triangle BCD$ according to SAS
2) Then, by CPCTC, $\overline{BE}\cong\overline{BD}$
Work Step by Step
*PLANNING:
1) First, prove that $\triangle BAE\cong\triangle BCD$ according to SAS
2) Then, by CPCTC, $\overline{BE}\cong\overline{BD}$
All the sides of a regular pentagon are equal and all the angles of a regular pentagon are equal.
1) $ABCDE$ is a regular pentagon. (Given)
2) $\overline{BA}\cong\overline{BC}$ and $\overline{AE}\cong\overline{CD}$ (in a regular pentagon, all the sides are equal; therefore, corresponding sides are congruent)
3) $\angle BAE\cong\angle BCD$ (in a regular pentagon, all the angles are equal; therefore, corresponding angles are congruent)
So now we have 2 sides and the included angle of $\triangle BAE$ are congruent with 2 corresponding sides and the included angle of $\triangle BCD$
4) $\triangle BAE\cong\triangle BCD$ (SAS)
5) $\overline{BE}\cong\overline{BD}$ (CPCTC)
