Question

Given: A, E, C, FAECF is a rhombus and start overline, E, B, end overline, \cong, start overline, F, D, end overline, .
EB
≅
FD
.

Prove: start overline, B, C, end overline, \cong, start overline, D, C, end overline
BC
≅
DC
.
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, E, C, FAECF is a rhombus
start overline, E, B, end overline, \cong, start overline, F, D, end overline
EB
≅
FD

Given. What are the last remaining steps in this question?

Answer 1

Fill in these final steps:

2. EC ≅ FC — All sides of a rhombus are congruent (AE = EC = CF = FA).
3. ∠ECB ≅ ∠FCD — the included angles of triangles CEB and CFD are congruent.
4. ΔCEB ≅ ΔCFD — SAS (EC ≅ FC from step 2, EB ≅ FD given, included angles from step 3).
5. BC ≅ DC — Corresponding parts of congruent triangles are congruent (CPCTC).

Thus BC ≅ DC.