Question

yz || wx and yz ≅ wx. complete the proof that wz ≅ xy. image of a quadrilateral wxyz with diagonal wy. table with statement and reason columns: 1. yz || wx (given), 2. yz ≅ wx (given), 3. ∠wyz ≅ ∠xwy (alternate interior angles theorem), 4. wy ≅ wy (reflexive property of congruence), 5. blank for statement blank for reason

Explanation:

Step1: Identify Congruent Triangles

We have \( \overline{YZ} \parallel \overline{WX} \), \( \overline{YZ} \cong \overline{WX} \), \( \angle WYZ \cong \angle XWY \) (alternate interior angles), and \( \overline{WY} \cong \overline{WY} \) (reflexive). So \( \triangle WYZ \cong \triangle XWY \) by SAS.

Step2: Corresponding Parts of Congruent Triangles

By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), \( \overline{WZ} \cong \overline{XY} \). So the statement for step 5 is \( \overline{WZ} \cong \overline{XY} \) and the reason is CPCTC.

Answer:

Statement 5: \( \overline{WZ} \cong \overline{XY} \); Reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)