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?

triangle angle sum theorem
quadrilateral angle sum theorem
definition of complementary
consecutive ∠s in a ▱ are supplementary
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The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.

Solve 2x+y=3 x+y=5 in substitution method

  cassidy wants to cut the yellow fabric into strips that are 0.3 yards wide. how many strips of yellow fabric can cassidy make? yellow fabric 16 yards for $108.00.