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.

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:

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answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)