Question

Somebody please help with this problem

Answer 1

Explanation:

We have been given that AE=BE and
`\angle1\cong \angle2`.

We can see that angle CEA is vertical angle of angle DEB, therefore,
`m\angle CEA=m\angle DEB` as vertical angles are congruent.

We can see in triangles CEA and DEF that two angles and included sides are congruent.

`\angle 1\cong \angle 2`

`AE=BE`

`\angle CEA\cong\angle DEB` or
`\angle 3\cong \angle 4`

Therefore,
`\Delta CEA\cong \Delta DEB` by ASA postulate.

Since corresponding parts of congruent triangles are congruent, therefore CE must be congruent to DE.