Question

Prove: Quadrilateral ABCD is a parallelogram.

Reason
Proof:
Statement
1. AC and BD bisect each other.
2. AE = EC
BE= ED
3. m_AEB = m_CED
4. AABE ACDE
given
definition of bisection
SAS criterion
5. LACD XL CAB
Corresponding angles of congruent
I triangles are congruent.
What is the reason for step 3 of this proof?
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

Answer 1

The reason for step 3 is option D

Explanation:

D. Vertical Angles Theorem

Answer 2

Step 3.

m∠ AEB = m∠ CED .........By Vertical Angles Theorem.

Explanation:

Vertical Angles Theorem:

Vertical angle theorem states that vertical angles, angles that are opposite each other and formed by two intersecting lines,are congruent.

If two lines intersect each other we have two pair of vertical opposite angles. As shown in the figure.

Here,

∠ 1 and ∠ 2 are vertical opposite angles and also they are equal.

∠ 3 and ∠ 4 are also vertical opposite angles and also they are equal.

For,

step 3. m∠ AEB = m∠ CED

Therefore, the reason for step 3 of this proof is Vertical Angles Theorem.