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Vlad1618 [11]
3 years ago
11

This is the question i need help with.​

Mathematics
1 answer:
bekas [8.4K]3 years ago
8 0

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.

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