Question 30 multiple choice Shizuku was asked to prove that

Question 30 (multiple choice)

Shizuku was asked to prove that the diagonals of a parallelogram bisect each other. Her response is below. What primary mistake did she make?

Quadrilateral WXYZ is a parallelogram.

Segments WX and YZ are parallel by the definition of a parallelogram.

Angles XVW and YVZ are congruent because vertical angles are congruent.

Angles WXZ and XZY are congruent because alternate interior angles are congruent.

Angles XWV and ZYV are congruent because of the Third Angles Theorem.

Therefore, ?XVW??ZVY by the ASA Congruence Theorem.

Since the definition of congruent triangles states that their corresponding parts are congruent,XV¯?ZV¯.

Likewise, WV¯?YV¯.

Due to the previous two statements and the definition of midpoint, V, must be the midpoint of XZ¯ and WY¯.

Therefore, by the definition of bisect, the diagonals bisect each other.

A) Shizuku did not show both pairs of opposite sides of the parallelogram are parallel in order to show congruent angles.

B) Shizuku did not write the proof in a two-column format, which is required for all proofs.

C) Shizuku used the conclusion of the theorem she\'s trying to prove as a statement in her proof of the theorem.

D) Shizuku has written a proof that is valid; she made no errors.

E) Shizuku did not show that one pair of congruent sides is necessary to use the Triangle Congruence Theorem

(E)Shizuka did not show that one pair of congruent sides is necessary to use the Triangle congruence Theorem