Answer:
Step-by-step explanation:
Given: WXYZ is a parallelogram, ZX ≅ WY
Prove: WXYZ is a rectangle
Proof:
Step 1. WXYZ is a parallelogram and ZX ≅ WY (Given)
Step 2. ZY ≅ WX (Opposite sides of parallelogram are congruent)
Step 3. YX ≅ YX (Reflexive Property)
Step 4. Consider △ZYX and △WXY, we have
ZX ≅ WY (Given)
ZY ≅ WX (Opposite sides of parallelogram are congruent)
YX ≅ YX (Reflexive Property)
Thus, by SSS rule, △ZYX ≅ △WXY
Step 5. By CPCTC, ∠ZYX ≅ ∠WXY
Step 6. m∠ZYX ≅ m∠WXY (Definition of congruency)
Step 7. m∠ZYX + m∠WXY = 180° ( consecutive ∠s in a parallelogram are supplementary)
Step 8. m∠ZYX + m∠ZYX = 180° (Substitution)
Step 9. 2(m∠ZYX) = 180° (Simplification)
Step 10. m∠ZYX = 90° (Dividing property of equality)
Step 11. WXYZ is a rectangle (Rectangle angle theorem)
Hence proved.
