# SOLUTION: determine whether quadrilateral MATH is a parallelogram, a rectangle, a rhombus, or a square given the vertices M (5,4), A (3, -6), T ( 0, -10), and H (2,0). Note: I keep comin

Algebra ->  Algebra  -> Polygons -> SOLUTION: determine whether quadrilateral MATH is a parallelogram, a rectangle, a rhombus, or a square given the vertices M (5,4), A (3, -6), T ( 0, -10), and H (2,0). Note: I keep comin      Log On

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 Geometry: Polygons Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Polygons Question 554928: determine whether quadrilateral MATH is a parallelogram, a rectangle, a rhombus, or a square given the vertices M (5,4), A (3, -6), T ( 0, -10), and H (2,0). Note: I keep coming up with an answer that doesn't make sense, the other problems, no problem.Found 2 solutions by Edwin McCravy, KMST:Answer by Edwin McCravy(8893)   (Show Source): You can put this solution on YOUR website!```Plot the points and draw the figure MATH: M(5,4), A(3,-6), T(0,-10), H(2,0). Lines are parallel if they have the same slope. A parallelogram is a quadrilateral with both pairs of oposite sides parallel. So we use the slope formula on all four sides. m = Slope of MA: M (5,4), A (3,-6), m = = = 5 Slope of TH: T(0,-10), and H(2,0). m = = = 5 So one pair of sides are parallel since both have slope 5. Slope of MH: M(5,4), H(2,0). m = = = Slope of AT: A(3,-6), T(0,-10), m = = = = So the other pair of sides are also parallel since both have slope . So MATH is a parallelogram. Edwin``` Answer by KMST(1868)   (Show Source): You can put this solution on YOUR website!We can calculate slopes of MA, AT, TH, HM, MT, and AH For MA, slope = For AT, slope = For TH, slope = For HM, slope = The fact that opposite sides of quadrilateral MATH have the same slope, means those pairs of opposite sides are parallel. That proves that it is a parallelogram. If the adjacent sides were perpendicular, we would have four right angles, and it would be a rectangle (or maybe even that special kind of rectangle that we call square). If the sides were perpendicular, the product of their slopes would be -1. However, is not -1. So, there are no right angles in MATH. Math is not a square or a rectangle. Could it be a rhombus? If it were a rhombus, the diagonals would be perpendicular. Let's calculate the slope of the diagonals For MT, slope = For AH, slope = The product of the slopes, , is not -1, so the diagonals are not perpendicular, and MATH is not a rhombus. Quadrilateral MATH is a parallelogram. It is neither a square, nor a rectangle, nor a rhombus.