Question

Given: A, B, C, DABCD is a rhombus.

Prove: triangle, A, E, B, \cong, triangle, C, E, B△AEB≅△CEB.
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
A, B, C, DABCD is a rhombus
Given
2
start overline, A, C, end overline
AC
and start overline, B, D, end overline
BD
bisect each other _

Answer 1

Step 1: ABCD is a rhombus. — Given.

Step 2: AC and BD bisect each other. — A rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other.

Step 3: AE = CE and BE = DE. — Definition of "bisect" (diagonals cut each other into equal segments).

Step 4: AB = BC. — All sides of a rhombus are congruent.

Step 5: BE = BE. — Reflexive property (common side).

Step 6: ΔAEB ≅ ΔCEB. — By SSS (AE = CE, AB = CB, BE = BE), the two triangles are congruent.

Therefore triangle AEB is congruent to triangle CEB.