Question

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

Given: A, B, C, DABCD is a parallelogram and start overline, F, E, end overline
FE
bisects start overline, A, C, end overline, .
AC
.

Prove: start overline, D, F, end overline, \cong, start overline, B, E, end overline
DF
≅
BE
.
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, F, E, end overline
FE
bisects start overline, A, C, end overline
AC

Given
2
angle, A, G, E, \cong, angle, C, G, F∠AGE≅∠CGF
Vertical angles are congruent
3
start overline, A, G, end overline, \cong, start overline, G, C, end overline
AG
≅
GC

A segment bisector divides a segment into two congruent segments
4
5
angle, G, A, E, \cong, angle, G, C, F∠GAE≅∠GCF
Parallel lines cut by a transversal form congruent alternate interior angles
6
triangle, A, G, E, \cong, triangle, C, G, F△AGE≅△CGF
ASA
7
start overline, A, E, end overline, \cong, start overline, C, F, end overline
AE
≅
CF

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
8
start overline, A, B, end overline, \cong, start overline, C, D, end overline
AB
≅
CD

Opposite sides of a parallelogram are congruent
9
start overline, D, F, end overline, \cong, start overline, B, E, end overline
DF
≅
BE

Congruent segments subtracted from congruent segments form congruent segments

Answer 1

Step 4 statement: AE ∥ CF

Step 4 reason: Opposite sides of a parallelogram are parallel.