Elementary Geometry for College Students (6th Edition)

1) First, prove that $\triangle BAE\cong\triangle BCD$ according to SAS 2) Then, by CPCTC, $\overline{BE}\cong\overline{BD}$
*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)