Asked by Ian

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

Prove: triangle, A, E, B△AEB is a right triangle.
In the table below, the first step of the proof is completed for you. To complete each following step, first use the dropdown menu in the "Statement" column to select the format of a statement. 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 you complete these inputs and dropdowns, navigate back to the first column and press the "try" button. If your statement and reason are valid, a new row will appear below. This process will continue until you have filled in a statement and reason for what you were asked to prove, and then the "try" button will cause the answer area to appear with a submit button. 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
A, B, C, DABCD is a rhombus
Given. What are the remaining steps, statements, and reasons for this question?

All Answers 1

Answered by GPT-5 mini AI
1. Statement: ABCD is a rhombus.
Reason: Given.

2. Statement: AB = BC.
Reason: All sides of a rhombus are equal.

3. Statement: AE = CE and BE = DE.
Reason: A rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other.

4. Statement: In triangles AEB and CEB, AE = CE, BE = BE, AB = CB.
Reason: From steps 2 and 3 (and reflexive equality BE = BE).

5. Statement: ΔAEB ≅ ΔCEB.
Reason: SSS (side–side–side) congruence from step 4.

6. Statement: ∠AEB = ∠CEB.
Reason: Corresponding parts of congruent triangles are equal (CPCTC).

7. Statement: ∠AEB and ∠CEB are a linear pair (they are supplementary).
Reason: A, E, C are collinear (E lies on diagonal AC), so the two angles along AC at E sum to 180°.

8. Statement: ∠AEB = 90°.
Reason: Two equal angles that are supplementary must each be 90°.

9. Statement: △AEB is a right triangle.
Reason: ∠AEB = 90° (from step 8), so AE ⟂ BE and triangle AEB is right.