Question

Given: WXYZ is a parallelogram, ZX ≅ WY

Answer 1

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.