Question

Given: AC and BD bisect each other.

Prove: BC || AD.
Step
1
2
3
4
5
6
7
Statement
AC and BD bisect each other
AE EC
BE ED
ZBEC LDEA
ABCE ADAE
ZBCE ZDAE
BC | AD
Reason
Given
156
of town lim
Property
onposite of congruent angles ar
The proof is complete. You may now press submit. You can still change reasons.
B
#H
E
D
C
two lines are parallel

Answer 1

It seems like you are trying to prove that two lines are parallel using angle bisectors. This is a common topic in geometry, and there are several methods and theorems that can help you with this task. One of them is the converse of the alternate interior angles theorem, which states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel1.

In your case, you are given that AC and BD bisect each other, which means that they divide each other into two equal parts. This implies that AE = EC and BE = ED. You can use these facts to write a proof using the two-column format, where you state the statements and reasons in each step. Here is one possible proof:

Statement Reason

1. AC and BD bisect each other Given

2. AE = EC and BE = ED Definition of bisector

3. ∠BEC ≅ ∠DEA Vertical angles are congruent

4. ΔABCE ≅ ΔADAE SAS congruence criterion

5. ∠BCE ≅ ∠DAE CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

6. BC

I hope this helps you understand how to prove that two lines are parallel using angle bisectors.