given: AB is congruent to AC: CD and BE are medians Prove; BE is congruent to CD.

Answer 1

Triangle ABC is isosceles by hypothesis.

Angle ABC = Angle ACE because the base angles of an isosceles triangle are equal

BD = EC because they are the the medians of equal sides

BC is common to triangles DBC and ECB

Therefore, Triangle DBC is congruent to triangle EBC because of SAS

BE = CD because they are corresponding parts of congruent triangles

QED