Question

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

Given: A, B, C, DABCD is a rectangle and start overline, A, F, end overline, \cong, start overline, D, G, end overline, .
AF
≅
DG
.

Prove: start overline, E, B, end overline, \cong, start overline, E, C, end overline
EB
≅
EC
.
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, F, end overline, \cong, start overline, D, G, end overline
AF
≅
DG

Given
2
start overline, F, G, end overline, \cong, start overline, F, G, end overline
FG
≅
FG

Reflexive Property
3
start overline, A, G, end overline, \cong, start overline, D, F, end overline
AG
≅
DF

Congruent segments added to congruent segments form congruent segments
4
angle, A, \cong, angle, D∠A≅∠D
In a rectangle, all angles are congruent
5
6
triangle, A, B, G, \cong, triangle, D, C, F△ABG≅△DCF
SAS
7
angle, A, B, G, \cong, angle, D, C, F∠ABG≅∠DCF
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
8
angle, A, B, C, \cong, angle, D, C, B∠ABC≅∠DCB
In a rectangle, all angles are congruent
9
angle, E, B, C, \cong, angle, E, C, B∠EBC≅∠ECB
Congruent angles subtracted from congruent angles form congruent angles
10
start overline, E, B, end overline, \cong, start overline, E, C, end overline
EB
≅
EC

In a triangle, sides opposite of congruent angles are congruent

Answer 1

Step 5 statement: AB ≅ DC

Reason: In a rectangle, opposite sides are congruent.