Consider the diagram and proof below. Given: WXYZ is a parallelogram, ZX ≅ WY Prove: WXYZ is a rectangle Parallelogram W X Y Z with diagonals is shown. Statement Reason 1. WXYZ is a ▱; ZX ≅ WY 1. Given 2. ZY ≅ WX 2. Opp. Sides of ▱ are ≅ 3. YX ≅ YX 3. Reflexive 4. △ZYX ≅ △WXY 4. SSS ≅ thm. 5. ∠ZYX ≅ ∠WXY 5. CPCTC 6. M∠ZYX ≅ m∠WXY 6. Def. Of ≅ 7. M∠ZYX m∠WXY = 180° 7. ? 8. M∠ZYX m∠ZYX = 180° 8. Substitution 9. 2(m∠ZYX) = 180° 9. Simplification 10. M∠ZYX = 90° 10. Div. Prop. Of equality 11. WXYZ is a rectangle 11. Rectangle ∠ thm. What is the missing reason in Step 7? triangle angle sum theorem quadrilateral angle sum theorem definition of complementary consecutive ∠s in a ▱ are supplementary.
