Question

Given: A, B, C, DABCD is a parallelogram and angle, A, \cong, angle, E, .∠A≅∠E.

Prove: start overline, C, D, end overline, \cong, start overline, C, E, end overline
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 the "Statement" column to select the format of a statement. Once you select a format, a statement will appear with input boxes and/or dropdowns to complete, and a dropdown menu will appear in the reason column. Once you complete these inputs and dropdowns, navigate back to the first column and press the "try" button. If your statement and reason are valid, a new row will appear below. This process will continue until you have filled in a statement and reason for what you were asked to prove, and then the "try" button will cause the answer area to appear with a submit button. The diagram associated with this problem is located below the proof table, and is available as a tactile printout. There may be a clarifying note below the diagram.
Step Statement Reason
1
A, B, C, DABCD is a parallelogram
angle, A, \cong, angle, E∠A≅∠E
Given. What are the correct remaining steps, statements, and reasons in this question. And please do them correctly.

Answer 1

I can finish the proof, but I need one missing piece of information: where is point E located in the figure? (Is E on BC, on AB, on AD, on an extension of one of these, or somewhere else? If you can paste or describe the diagram — e.g. “E lies on line BC with B between C and E” — I will give the exact step-by-step table.)

Without the diagram I can only give the general plan (the exact angle-equality step that makes triangle CDE isosceles depends on E’s position). The general approach is:

1. ABCD is a parallelogram and ∠A ≅ ∠E. — Given.
2. AB ∥ CD and AD ∥ BC. — Definition of parallelogram.
3. ∠A ≅ ∠C. — Opposite angles of a parallelogram are congruent (or from parallel lines).
4. ∠C ≅ ∠E. — Transitive: ∠A ≅ ∠E and ∠A ≅ ∠C imply ∠C ≅ ∠E.
5. Use the parallel-line/collinearity information (step 2) and the position of E to identify two angles in triangle CDE that are equal (this is the step I need the diagram to make precise). Conclude in triangle CDE that the two base angles are congruent.
6. CD ≅ CE. — In a triangle, congruent base angles imply the opposite sides are congruent.

If you tell me exactly where E lies (or upload / describe the diagram), I will convert that outline into the precise statements and reasons in the table format required.