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.