Question

Consider the diagram and proof below. Given: WXYZ is a parallelogram, ZX ≅ WY Prove: WXYZ is a rectangle 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?

Answer 1

D. consecutive ∠s in a ▱ are supplementary

Explanation:

It's Was D for me.

Got Correct On MyPath.

Answer 2

Answer: The missing reason in Step 7 is ' Consecutive interior angles add up to 180°'

Step-by-step explanation:

Since we know that, The sum of two consecutive interior angles made by same transversal on two parallel lines is always equal to 180°.

And, here
`ZY\parallel WX` and XY is the common transversal, Also, ∠WYX and ∠WXY are the consecutive angles on lines ZY and WX respectively by transversal YX. ( shown on figure)

Therefore, m∠ZYX + m∠WXY = 180°

Here, Given, WXYZ is a parallelogram in which
`ZX\cong WY`

we have to prove that: WXYZ is a rectangle.

Statement Reason

1. WXYZ is a parallelogram, 1. Given

ZX ≅WY

2. ZY ≅ WX 2. opposite sides of parallelogram

are congruent.

3. YX≅YX 3. Reflexive

4. ΔZYX ≅ Δ WXY 4. SSS postulate of congruence

5. ∠ZYX ≅ ∠WXY 5. CPCTC

6. m∠ZYX ≅ m∠WXY 6. definition of congruence.

7.m∠ZYX + m∠WXY = 180° 7.Consecutive interior

angles add up to 180°'

8.m∠ZYX + m∠ZYX = 180° 8. By substitution

9. 2(m∠ZYX) = 180° 9. By simplification

10.m∠ZYX = 90° 10.division property of equality

11. WXYZ is a rectangle 11.Rectangle angle theorem.