Question

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.

Answer 1

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:

https://brainly.com/question/14626404

Answer 2

Answer:

edge answer 2021

Step-by-step explanation: