Question

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

Given: A, B, C, DABCD is a parallelogram, EE is the midpoint of start overline, A, B, end overline
AB
and FF is the midpoint of start overline, D, C, end overline, .
DC
.

Prove: start overline, D, E, end overline, \cong, start overline, F, B, end overline
DE
≅
FB
.
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
EE is the midpoint of start overline, A, B, end overline
AB

FF is the midpoint of start overline, D, C, end overline
DC

Given
2
start overline, A, D, end overline, \cong, start overline, C, B, end overline
AD
≅
CB

Opposite sides of a parallelogram are congruent
3
start overline, D, C, end overline, \cong, start overline, A, B, end overline
DC
≅
AB

Opposite sides of a parallelogram are congruent
4
F, C, equals, one half, D, CFC=
2
1
​
DC
When a midpoint divides a segment into two parts, each part is half the length of the whole segment
5
6
start overline, F, C, end overline, \cong, start overline, A, E, end overline
FC
≅
AE

Segments that are half the lengths of congruent segments are congruent
7
angle, A, \cong, angle, C∠A≅∠C
Opposite angles of a parallelogram are congruent
8
triangle, A, D, E, \cong, triangle, C, B, F△ADE≅△CBF
SAS
9
start overline, D, E, end overline, \cong, start overline, F, B, end overline
DE
≅
FB

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Answer 1

Step 5 statement: AE = 1/2 AB

Step 5 reason: When a midpoint divides a segment into two parts, each part is half the length of the whole segment.