Question

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

Given: A, E, C, FAECF is a rhombus and start overline, E, B, end overline, \cong, start overline, F, D, end overline, .
EB
≅
FD
.

Prove: triangle, A, B, C, \cong, triangle, A, D, C△ABC≅△ADC.
Step Statement Reason
1
A, E, C, FAECF is a rhombus
start overline, E, B, end overline, \cong, start overline, F, D, end overline
EB
≅
FD

Given
2
start overline, A, E, end overline, \cong, start overline, A, F, end overline
AE
≅
AF

All sides of a rhombus are congruent
3
start overline, A, B, end overline, \cong, start overline, A, D, end overline
AB
≅
AD

Congruent segments added to congruent segments form congruent segments
4
start overline, C, A, end overline
CA
bisects angle, E, A, F∠EAF
The diagonals of a rhombus bisect the interior angles
5
6
start overline, A, C, end overline, \cong, start overline, A, C, end overline
AC
≅
AC

Reflexive Property
7
triangle, A, B, C, \cong, triangle, A, D, C△ABC≅△ADC
SAS

Answer 1

Step 5 (statement): ∠BAC ≅ ∠CAD

Step 5 (reason): From 4, AC bisects ∠EAF so ∠EAC ≅ ∠CAF. Because B is collinear with E and D is collinear with F, ∠EAC = ∠BAC and ∠CAF = ∠CAD; hence ∠BAC ≅ ∠CAD.