Question

Given: ABCD is a parallelogram and ∠A≅∠E.
Prove: CD ≅ CE.
In the table below, the first step of the proof is completed for you. To complete each following step, first use the dropdown menu in
1. ABCD is a parallelogram. ∠A≅∠E.
Reason: Given.

Answer 1

I don’t have the diagram or the location of point E. I need that to finish the table correctly — the angle- and side-relations you can use depend on whether E is on AB, AD, BC, an extension of one of those, etc.

Can you either
- paste the diagram (or a clear description where E lies), or
- confirm the original statement (maybe it was CD ≅ DE rather than CD ≅ CE)?

If you want the general proof strategy (you can adapt it once you tell me where E is):
- From "ABCD is a parallelogram" deduce AB ∥ CD and AD ∥ BC.
- Use the parallel-line angle relationships (or the parallelogram opposite-angle property) to relate ∠A to one of the angles at C or D.
- Combine that relation with the given ∠A ≅ ∠E to get two equal angles in triangle CDE (specifically you need ∠D ≅ ∠E to conclude CD ≅ CE).
- Then apply the Isosceles Triangle Theorem (if two base angles are equal, the opposite sides are equal) to conclude CD ≅ CE.

Send the diagram or specify where E is and I will fill in the exact table steps and reasons.