SOLUTION: 8. solve for x: (3 + 2i) + (4 + xi) = 7 - 5i 9. Which of the following is not sufficient to prove that a quadrilateral is a parallelogram? (1) opposite sides are congruent (

Question 173132This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: 8. solve for x: (3 + 2i) + (4 + xi) = 7 - 5i
9. Which of the following is not sufficient to prove that a quadrilateral is a parallelogram?
(1) opposite sides are congruent (2) opposite angles are congruent
(3) diagonals are congruent (4) consecutive angles are supplementary

Show work please, thank you!This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B

Found 2 solutions by stanbon, user_dude2008:
Answer by stanbon(48564) (Show Source):
You can put this solution on YOUR website!
8. solve for x: (3 + 2i) + (4 + xi) = 7 - 5i
7 + (2+x)i = 7 - 5i
2+x = 5
x = 3
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9. Which of the following is not sufficient to prove that a quadrilateral is a parallelogram?
(1) opposite sides are congruent (2) opposite angles are congruent
(3) diagonals are congruent (4) consecutive angles are supplementary
Draw the pictures of the various conditions; see if you get a parallelogram
under each condition.
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Cheers,
Stan H.

Answer by user_dude2008(1825) (Show Source):
You can put this solution on YOUR website!
8)

(3 + 2i) + (4 + xi) = 7 - 5i

(3 + 4) + (2i + xi) = 7 - 5i

-----> 3+4 = 7 and 2i+xi=5i

2i+xi=-5i

xi=-7i

x=-7 <----answer

9)

Which of the following is not sufficient to prove that a quadrilateral is a parallelogram?

The answer is (4) consecutive angles are supplementary

Example:

Draw a trapezoid with the top and bottom parallel. Now make one side completely vertical. This will make 2 consecutive angles that add to 180, but it won't be a parallelogram