document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #361576 by KMST(5328)\"\" \"About 
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We can calculate slopes of MA, AT, TH, HM, MT, and AH
\n" ); document.write( "For MA, slope = \"%284-%28-6%29%29%2F%285-3%29=10%2F2=5\"
\n" ); document.write( "For AT, slope = \"%28-6-%28-10%29%29%2F%283-0%29=4%2F3\"
\n" ); document.write( "For TH, slope = \"%280-%28-10%29%29%2F%282-0%29=10%2F2=5\"
\n" ); document.write( "For HM, slope = \"%284-0%29%2F%285-2%29=4%2F3\"
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "However, \"%285%29%284%2F3%29=20%2F3\" is not -1. So, there are no right angles in MATH. Math is not a square or a rectangle.
\n" ); document.write( "Could it be a rhombus? If it were a rhombus, the diagonals would be perpendicular.
\n" ); document.write( "Let's calculate the slope of the diagonals
\n" ); document.write( "For MT, slope = \"%284-%28-10%29%29%2F%285-0%29=14%2F5\"
\n" ); document.write( "For AH, slope = \"%28-6-0%29%2F%283-2%29=-6%2F1=-6\"
\n" ); document.write( "The product of the slopes, \"-6%2814%2F5%29=-84%2F5\" , is not -1, so the diagonals are not perpendicular, and MATH is not a rhombus.
\n" ); document.write( "Quadrilateral MATH is a parallelogram. It is neither a square, nor a rectangle, nor a rhombus. \n" ); document.write( "
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