Given: wxyz is a parallelogram, zx ≅ wy prove: wxyz is a rectangle what is the missing reason in step 7? a. triangle angle sum theorem. b. quadrilateral angle sum theorem. c. definition of complementary. d. consecutive ∠s in a ▱ are supplementary. 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.

The correct option for the missing statement of Step 7 of the two column proof is option D.

D. Consecutive ∠s in a parallelogram are supplementary

The reason for the above selection is presented as follows;

The given two column proof is presented as follows;

Statement                                Reason

1. WXYZ is a parallelogram; ZX ≅ WY       1. Given

2. ZY ≅ WX                                 2. Opp. sides of parallelogram are ≅

3. YX ≅ YX                                  3. Reflexive property

4. ΔZYX ≅ ΔWXY                        4. SSS ≅ thm.

5. ∠ZYX ≅ ∠WXY                      5. CPCTC

6. m∠ZYX ≅ m∠WXY                 6. Def. of ≅

7. m∠ZYX + m∠WXY = 180°      7. Consecutive ∠s in a parallelogram are supplementary

8. m∠ZYX + m∠ZYX = 180°       8. Supplementary property

9. 2(m∠ZYX) = 180°                    9. Simplification

10. m∠ZYX = 90°                        10. Division Property of equality

11. WXYZ is a rectangle             11. Rectangle ∠ theorem

Where;

Def = Definition

Opp. = Opposite

≅ = Congruent

CPCTC = Congruent Parts of Congruent Triangles are Congruent

The missing reason is that in a parallelogram, consecutive angles are supplementary

Learn more about parallelograms here:

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