Prove: Quadrilateral ABCD is a parallelogram.ReasonProof:Statement1. AC and BD bisect each other.2. AE = ECBE= ED3. m_AEB = m_CED4. AABE ACDEgivendefinition of bisectionSAS criterion5. LACD XL CABCorresponding angles of congruentI triangles are congruent.What is the reason for step 3 of this proof?A. Alternate Interior Angles TheoremB. Corresponding angles in congruent triangles are congruent.C. For parallel lines cut by a transversal, corresponding angles are congruent.D. Vertical Angles TheoremE. SAS criterion for congruence

Accepted Solution

Answer:Step 3.m∠ AEB = m∠ CED .........By  Vertical Angles Theorem.Step-by-step 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.