Question

Given: start overline, B, E, end overline, \cong, start overline, C, E, end overline
BE
≅
CE
and start overline, B, C, end overline, \parallel, start overline, A, D, end overline, .
BC
∥
AD
.

Prove: angle, B, C, E, \cong, angle, A, D, E∠BCE≅∠ADE.
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
start overline, B, E, end overline, \cong, start overline, C, E, end overline
BE
≅
CE

start overline, B, C, end overline, \parallel, start overline, A, D, end overline
BC
∥
AD

Given
2
angle, E, B, C, \cong, angle, B, C, E∠EBC≅∠BCE
In a triangle, angles opposite of congruent sides are congruent
3
angle, E, B, C, \cong, angle, A, D, E∠EBC≅∠ADE
Parallel lines cut by a transversal form congruent alternate interior angles. What are the last remaining steps for this question?

Answer 1

Step 3 (already shown): ∠EBC ≅ ∠ADE — Parallel lines cut by a transversal form congruent alternate interior angles.

Step 4: ∠BCE ≅ ∠ADE — If two angles are congruent to the same angle, then they are congruent to each other (transitive property of congruence).