Question

select the correct answer from each drop-down menu.
complete the following proof.
given: wxyz is a parallelogram with diagonals \\(\overline{xz}\\) and \\(\overline{wy}\\) intersecting at point v.
prove: \\(\overline{xz}\\) bisects \\(\overline{wy}\\)
image of parallelogram wxyz with diagonals intersecting at v

statements	reasons
2. \\(\overline{wx} \parallel \overline{zy}\\) and \\(\overline{xy} \parallel \overline{wz}\\)	definition of a parallelogram
3. \\(\angle wxy \cong \angle yzw\\) \\(\angle wxz \cong \angle yzx\\)	drop-down menu
4. \\(\overline{xy} \cong \overline{zw}\\)	opposite sides of a parallelogram are congruent
5. \\(\triangle wzv \cong \triangle yxv\\)	drop-down menu with options: sas congruency criteria, sss congruency criteria, ssa congruency criteria, asa congruency criteria
6. \\(\overline{wv} \cong \overline{yv}\\)	reasons column, partially visible
7. \\(\overline{xz}\\) bisects \\(\overline{wy}\\)	reasons column, partially visible

Explanation:

Step1: Analyze Step 3

In a parallelogram, \( \overline{WX} \parallel \overline{ZY} \) and \( \overline{XY} \parallel \overline{WZ} \). When a transversal (like \( \overline{XZ} \)) intersects parallel lines, alternate interior angles are congruent. So \( \angle WXY \cong \angle YZW \) and \( \angle WXZ \cong \angle YZX \) follow from the Alternate Interior Angles Theorem.

Step2: Analyze Step 5

We have \( \angle WXZ \cong \angle YZX \) (from step 3), \( \overline{XY} \cong \overline{ZW} \) (from step 4), and \( \angle WZX \cong \angle YXV \) (alternate interior angles from \( \overline{WZ} \parallel \overline{XY} \)). This matches the ASA (Angle - Side - Angle) congruency criteria, so \( \triangle WZV \cong \triangle YXV \) by ASA.

Answer:

For step 3 reason: Alternate Interior Angles Theorem
For step 5 reason: ASA congruency criteria