Question

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

Given: A, B, C, DABCD is a rectangle and start overline, A, E, end overline, \cong, start overline, D, E, end overline, .
AE
≅
DE
.

Prove: start overline, B, E, end overline, \cong, start overline, C, E, end overline
BE
≅
CE
.
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 rectangle
start overline, A, E, end overline, \cong, start overline, D, E, end overline
AE
≅
DE

Given
2
start overline, A, B, end overline, \cong, start overline, D, C, end overline
AB
≅
DC

Opposite sides of a rectangle are congruent
3 type of statement
4
angle, B, A, F, \cong, angle, C, D, G∠BAF≅∠CDG
In a rectangle, all angles are congruent
5
angle, B, A, E, \cong, angle, C, D, E∠BAE≅∠CDE
Congruent angles added to congruent angles form congruent angles
6
triangle, B, A, E, \cong, triangle, C, D, E△BAE≅△CDE
SAS
7
start overline, B, E, end overline, \cong, start overline, C, E, end overline
BE
≅
CE

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Answer 1

Statement (step 3): A, E, D are collinear.
Reason: E is the midpoint of AD (from AE ≅ DE) — definition of midpoint (so A, E, D are collinear).