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Given the vertices E-2 -1 F-4 3 G1 5 and H3 1 Determine the best classification for this quadrilateral?
Wiki User
∙ 15y ago
Vertices: E (-2, -1); F (-4, 3); G (1, 5); and H (3, 1).
Plot these points in a coordinate system and connect them. The quadrilateral EFGH is formed.
The slope of the line where the side EF lies is -2.
[(3 - -1)/(-4 - -2)] = 4/-2 = -2
The slope of the line where the side HG lies is -2.
[(5 - 1)/(1 - 3)] = 4/-2 = -2
Thus the opposite sides EF and HG of the quadrilateral EFGH are parallel.
The slope of the line where the side EH lies is 2/5.
[(1 - -1)/(3 - -2)] = 2/5
The slope of the line where the side FG lies is 2/5.
[(5 - 3)/(1 - -4)] = 2/5
Thus the opposite sides EH and FG of the quadrilateral EFGH are parallel.
Since any of the slopes is not a negative reciprocal of the others, then the two adjacent sides are not perpendicular. And if we look at the diagram, we clearly see that this quadrilateral can be a parallelogram.
The length of the side EF is square root of 20.
Square root of [(5 - 1)^2 + (1 - 3)^2] = Square root of [4^2 + (-2)^2] = Square root of 20.
The length of the side HG is square root of 20.
Square root of [(3 - -1)^2 + (-4 - -2)^2] = Square root of [4^2 + (-2)^2] = Square root of 20.
Thus, the opposite sides EF and HG of the quadrilateral EFGH are congruent.
Two other parallel sides, EH and FG, must be congruent also, since they intersect two other parallel lines (their length is equal to square root of 29).
So we verified that the quadrilateral EFGH is a parallelogram.
Wiki User
∙ 15y ago
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