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

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.

Answer 2

Answer:

D   took the quiz on edge   hope this helps!   :)

Step-by-step explanation:

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