Question

Given: A, B, C, DABCD is a parallelogram and F, B, E, DFBED is a parallelogram.

Prove: triangle, F, A, B, \cong, triangle, E, C, D△FAB≅△ECD.
In the proof shown in the table below, the statements and the first reason are filled in for you. Use the dropdown menu in the Reason column to select the reason for the next statement. Once you have selected a reason, a new statement will appear in a new row below. This will continue until you have selected the reason for the final statement, and then the answer area will appear with a submit button. The diagram associated with this problem is located at the bottom of the page, below the proof, 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
F, B, E, DFBED is a parallelogram
Given
2
start overline, F, B, end overline, \cong, start overline, E, D, end overline
FB
≅
ED
_

Answer 1

1. ABCD is a parallelogram; DFBE is a parallelogram. — Given.

2. FB ≅ ED. — Opposite sides of a parallelogram are congruent (in parallelogram DFBE).

3. AB ≅ CD. — Opposite sides of a parallelogram are congruent (in parallelogram ABCD).

4. ∠FBA ≅ ∠EDC. — FB ∥ ED and BA ∥ DC (parallelogram opposite sides are parallel), so the angle formed by FB and BA equals the angle formed by ED and DC (corresponding/alternate interior angles from parallel lines).

5. ΔFAB ≅ ΔECD. — By SAS (FB ≅ ED, AB ≅ CD, and included angles ∠FBA ≅ ∠EDC).