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

false

step-by-step explanation:

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol