Question

Given: start overline, A, B, end overline, \cong, start overline, C, D, end overline, comma
AB
≅
CD
, start overline, A, D, end overline, \parallel, start overline, B, C, end overline, comma
AD
∥
BC
, start overline, B, G, end overline, \cong, start overline, H, D, end overline, comma
BG
≅
HD
, angle, C, G, E, \cong, angle, A, H, F∠CGE≅∠AHF and start overline, A, E, end overline, \cong, start overline, F, C, end overline, .
AE
≅
FC
.

Prove: angle, B, A, E, \cong, angle, D, C, F∠BAE≅∠DCF.
In the proof shown in the table below, the statements and the first reason are filled in for you. Use the dropdown menu in the Reason column to select the reason for the next statement. Once you have selected a reason, a new statement will appear in a new row below. This will continue until you have selected the reason for the final statement, and then the answer area will appear with a submit button. The diagram associated with this problem is located at the bottom of the page, below the proof, and is available as a tactile printout. There may be a clarifying note below the diagram.
Step Statement Reason
1
start overline, A, B, end overline, \cong, start overline, C, D, end overline
AB
≅
CD

start overline, A, D, end overline, \parallel, start overline, B, C, end overline
AD
∥
BC

start overline, B, G, end overline, \cong, start overline, H, D, end overline
BG
≅
HD

angle, C, G, E, \cong, angle, A, H, F∠CGE≅∠AHF
start overline, A, E, end overline, \cong, start overline, F, C, end overline
AE
≅
FC

Given
2
start overline, E, F, end overline, \cong, start overline, E, F, end overline
EF
≅
EF


Reflexive Property
3 select a reason
start overline, A, F, end overline, \cong, start overline, C, E, end overline
AF
≅
CE

Answer 1

Reason: Corresponding parts of congruent triangles (CPCTC).