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?

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 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

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.

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 ≅ WY1.given

2.ZY ≅ WX2.opp. sides of ▱ are ≅

3.YX ≅ YX3.reflexive

4.△ZYX ≅ △WXY4.SSS ≅ thm.

5.∠ZYX ≅ ∠WXY5.CPCTC

6.m∠ZYX ≅ m∠WXY6.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 rectangle11.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