Given:
[tex]\overline{AE}\cong \overline{DE}, \overline{AB}\cong \overline{DC}[/tex]
To prove:
[tex]\Delta ABE\cong \Delta DCE[/tex]
Solution:
In triangle AED,
[tex]\overline{AE}\cong \overline{DE}[/tex]
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,
[tex]\angle A\cong \angle D[/tex]
In triangle ABE and triangle DCE,
[tex]\overline{AE}\cong \overline{DE}[/tex] (Given)
[tex]\angle A\cong \angle D[/tex] (Base angles of an isosceles triangle are equal)
[tex]\overline{AB}\cong \overline{DC}[/tex] (Given)
Two corresponding sides and their included angles are congruent. So, triangles are congruent by SAS postulate of congruence.
[tex]\Delta ABE\cong \Delta DCE[/tex] (By SAS postulate of congruence)
Hence proved.
