What is the reason for step 3 of this proof

Asked by maham237 @ 21/05/2021 in Mathematics viewed by 401 People

Given: and bisect each other.

Prove: Quadrilateral ABCD is a parallelogram.

Proof:
Statement Reason
1. and bisect each other. given
2. AE = EC
BE = ED definition of bisection
3. mAEB = mCED
4. ABE CDE SAS criterion
5. ACD CAB Corresponding angles of congruent triangles are congruent.
6. converse of Alternate Interior Angles Theorem
7. mBEC = mAED Vertical Angles Theorem
8. BEC DEA SAS criterion for congruence
9. DBC BDA Corresponding angles of congruent triangles are congruent.
10. converse of Alternate Interior Angles Theorem
11. Quadrilateral ABCD is a parallelogram. definition of a parallelogram

a Alternate Interior Angles Theorem
B. Corresponding angles in congruent triangles are congruent.

C. For parallel lines cut by a transversal, corresponding angles are congruent.

D. Vertical Angles Theorem

E. SAS criterion for congruence

Answered by maham237 @ 21/05/2021

We have to prove that Quadrilateral ABCD is a parallelogram.

The third step is m AEB = mCED

As ABCD is a quadrilateral, the point of intersection of diagonals being E.

In the first step while proving it is written that Diagonals bisect each other i.e

AE = EC and BE= ED

After drawing the quadrilateral it is being found that ∠AEB and ∠CED are vertically opposite angles.

Out of the given five options option (D) is the correct option. which is vertical angles theorem.

vertical angle theorem states that if two lines intersect at a point ,then their vertically opposite angles are equal.

What is the reason for step 3 of this proof

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