# [Solved] Consider the diagram and proof below. Given: WXYZ is a parallelogram, ZX ≅ WY Prove: WXYZ is a rectangle Parallelogram

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

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