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 start overline, B, D, end overline, is perpendicular to, start overline, A, C, end overline, .
BD
⊥
AC
.

Prove: triangle, A, B, E, \cong, triangle, C, B, E△ABE≅△CBE.
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

start overline, B, D, end overline, is perpendicular to, start overline, A, C, end overline
BD
⊥
AC

Given
2
angle, A, E, B∠AEB is a right angle
Perpendicular lines form right angles
3 triangle△
\cong≅ triangle△
✕
4
angle, A, E, B, \cong, angle, C, E, B∠AEB≅∠CEB
All right angles are congruent
5
start overline, A, E, end overline, \cong, start overline, C, E, end overline
AE
≅
CE

A segment bisector divides a segment into two congruent segments
6
start overline, B, E, end overline, \cong, start overline, B, E, end overline
BE
≅
BE

Reflexive Property
7
triangle, A, B, E, \cong, triangle, C, B, E△ABE≅△CBE
SAS

select a reason for step 3 SSS SAS ASA AAS SSA AA HL

Answer 1

Missing step (Step 3):
Statement: ∠CEB is a right angle.
Reason: Perpendicular lines form right angles.