Question

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

Prove: triangle, A, C, B, \cong, triangle, D, B, C△ACB≅△DBC.
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 square
Given. What are the remaining steps, statements, and reasons for this question? And please do them correctly!

Answer 1

1. ABCD is a square. — Given.

2. AB = BC = CD = DA. — Definition of square (all four sides are equal).

3. ABCD is a rectangle. — Definition of square (all interior angles are right), so it satisfies the definition of a rectangle.

4. AC = BD. — Diagonals of a rectangle are congruent.

5. BC = BC. — Common side (reflexive property).

6. AB = CD. — From step 2 (all sides of the square are equal).

7. △ACB ≅ △DBC. — SSS (AC = BD from step 4, CB = BC from step 5, AB = CD from step 6).

Therefore triangles ACB and DBC are congruent.