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Pre-Calculus Homework Solutions 250

# Pre-Calculus Homework Solutions 250 - parallelogram Use the...

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parallelogram. Use the Distance Formula to determine whether the opposite sides are congruent. AD ¬ ( x 2 x 1 ) 2 ( y 2 y 1 ) 2 ¬ [ 4 ( 5)] 2 [2 ( 4)] 2 ¬ 37 BC ¬ (4 3) 2 [4 ( 2)] 2 ¬ 37 AB ¬ [3 ( 5)] 2 [ 2 ( 4)] 2 ¬ 68 CD ¬ ( 4 4) 2 (2 4) 2 ¬ 68 Since the measures of both pairs of opposite sides are equal, ABCD is a parallelogram. 28. Yes; If the midpoints of the diagonals are the same, the diagonals bisect each other. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Find the midpoints of WY and XZ . WY : x 1 2 x 2 , y 1 2 y 2 ¬ 6 2 0 , 5 2 ( 1) ¬ ( 3, 3) XZ : x 1 2 x 2 , y 1 2 y 2 ¬ 1 2 ( 5) , 4 2 ( 2) ¬ ( 3, 3) The midpoints of WY and XZ are the same, so WXYZ is a parallelogram. 29. No; First use the Distance Formula to determine whether the opposite sides are congruent. GH ¬ ( x 2 x 1 ) 2 ( y 2 y 1 ) 2 ¬ [4 ( 2)] 2 (4 8) 2 ¬ 52 JK ¬ ( 1 6) 2 [ 7 ( 3)] 2 ¬ 65 Since GH JK , GH JK . Therefore, GHJK is not a parallelogram. 30. No; If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Use the Distance Formula to determine whether the opposite sides are congruent. HJ ¬ ( x 2 x 1 ) 2 ( y
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