Question

Given: triangle, F, B, E, \cong, triangle, D, C, E, comma△FBE≅△DCE, start overline, A, D, end overline, \cong, start overline, B, C, end overline
AD
≅
BC
and BB is the midpoint of start overline, A, F, end overline, .
AF
.

Prove: A, B, C, DABCD is a parallelogram.
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
triangle, F, B, E, \cong, triangle, D, C, E△FBE≅△DCE
start overline, A, D, end overline, \cong, start overline, B, C, end overline
AD
≅
BC

BB is the midpoint of start overline, A, F, end overline
AF

Given
2
start overline, A, B, end overline, \cong, start overline, B, F, end overline
AB
≅
BF
_

Answer 1

Step 1: △FBE ≅ △DCE; AD ≅ BC; B is the midpoint of AF. — Given

Step 2: AB ≅ BF. — Definition of midpoint

Step 3: BF ≅ DC. — Corresponding parts of congruent triangles are congruent (CPCTC) from △FBE ≅ △DCE

Step 4: AB ≅ DC. — Transitive property of segment congruence (AB ≅ BF and BF ≅ DC)

Step 5: AD ≅ BC and AB ≅ DC, so both pairs of opposite sides of quadrilateral ABCD are congruent. — From given and Step 4

Step 6: ABCD is a parallelogram. — If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram