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Pre-Calculus Homework Solutions 248

# Pre-Calculus Homework Solutions 248 - Since opposite sides...

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Since opposite sides have the same slope, B w C w i D w E w and B w E w i C w D w . Therefore, BCDE is a parallelogram by definition. 9. Yes; First use the Distance Formula to determine whether the opposite sides are congruent. AD 5 Ï ( x 2 2 w x 1 ) 2 1 w ( y 2 2 w y 1 ) 2 w 5 Ï [ 2 6 2 w ( 2 4)] w 2 1 (3 w 2 0) 2 w 5 Ï 13 w BC 5 Ï (1 2 3 w ) 2 1 (4 w 2 1) 2 w 5 Ï 13 w Since AD 5 BC , A w D w > B w C w . Next, use the Slope Formula to determine whether A w D w i B w C w . slope of A w D w 5 } y x 2 2 2 2 y x 1 1 } 5 } 2 6 3 2 2 ( 0 2 4) } 52 } 3 2 } slope of B w C w 5 } 4 1 2 2 1 3 } } 3 2 } A w D w and B w C w have the same slope, so they are parallel. Since one pair of opposite sides is congruent and parallel, ABCD is a parallelogram. 10. No; 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 E w G w and F w H w .
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