Question

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

Given: start overline, B, D, end overline
BD
bisects start overline, A, C, end overline
AC
and angle, C, B, E, \cong, angle, A, D, E, .∠CBE≅∠ADE.

Prove: A, B, C, DABCD is a parallelogram.
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
start overline, B, D, end overline
BD
bisects start overline, A, C, end overline
AC

angle, C, B, E, \cong, angle, A, D, E∠CBE≅∠ADE
Given
2
start overline, B, C, end overline, \parallel, start overline, A, D, end overline
BC
∥
AD

If two lines cut by a transversal form congruent alternate interior angles, then the two lines are parallel
3 type of statement
4
angle, B, E, C, \cong, angle, D, E, A∠BEC≅∠DEA
Vertical angles are congruent
5
triangle, B, E, C, \cong, triangle, D, E, A△BEC≅△DEA
AAS
6
start overline, B, C, end overline, \cong, start overline, A, D, end overline
BC
≅
AD

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
7
A, B, C, DABCD is a parallelogram
A, B, C, DABCD is a parallelogram because it is a quadrilateral with one pair of opposite sides parallel and congruent

Answer 1

Step 3 statement: EC ≅ EA

Reason: BD bisects AC (definition of bisector / midpoint), so AE = EC.