Question

This is the question i need help with.​

Answer 1

Given:

$\overline{AE}\cong \overline{DE}, \overline{AB}\cong \overline{DC}$

To prove:

$\Delta ABE\cong \Delta DCE$

Solution:

In triangle AED,

$\overline{AE}\cong \overline{DE}$

Two sides of triangle AED are equal, it means triangle AED is an isosceles triangle. The base angles of an isosceles triangle are equal. So,

$\angle A\cong \angle D$

In triangle ABE and triangle DCE,

$\overline{AE}\cong \overline{DE}$         (Given)

$\angle A\cong \angle D$        (Base angles of an isosceles triangle are equal)

$\overline{AB}\cong \overline{DC}$        (Given)

Two corresponding sides and their included angles are congruent. So, triangles are congruent by SAS postulate of congruence.

$\Delta ABE\cong \Delta DCE$           (By SAS postulate of congruence)

Hence proved.