Question

Fill in the missing statement and reason of the proof below.

Given: A, B, C, DABCD is a parallelogram and start overline, C, E, end overline, \cong, start overline, F, A, end overline, .
CE
≅
FA
.

Prove: F, B, E, DFBED is a parallelogram.
In the proof shown in the table below, one of the steps in the middle is missing. Before completing the missing step, make sure to read the steps that come after it. To complete the missing step, first use the dropdown menu in the statement column to select the format of the statement for that step. 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 completed, press the submit button in the answer area at the bottom of the page. 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
start overline, C, E, end overline, \cong, start overline, F, A, end overline
CE
≅
FA

Given
2 type of statement
3
start overline, B, E, end overline, \cong, start overline, F, D, end overline
BE
≅
FD

Congruent segments added to congruent segments form congruent segments
4
start overline, B, C, end overline, \parallel, start overline, A, D, end overline
BC
∥
AD

Opposite sides of a parallelogram are parallel
5
start overline, B, E, end overline, \parallel, start overline, F, D, end overline
BE
∥
FD

Segments that are colinear with parallel segments are parallel
6
F, B, E, DFBED is a parallelogram
F, B, E, DFBED is a parallelogram because it is a quadrilateral with one pair of opposite sides parallel and congruent

Answer 1

Step 2 statement: BC ≅ AD

Reason: Opposite sides of a parallelogram are congruent.