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Geometry, Quadrilaterals - May 06, 2005
The GMAT Math practice question for the day is a question on polygons and their shapes in geometry
Question
Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral?
A. Square
B. Rectangle but not a square
C. Rhombus
D. Parallelogram but not a rhombus
E. Kite
The correct choice is (C) and the correct answer is Rhombus.
Explanatory Answer
The lengths of the four sides, AB, BC, CD and DA are all equal to  . Hence, the given quadrilateral is either a Rhombus or a Square.
Now let us compute the lengths of the two diagonals AC and BD. The length of AC is  and the length of BD is  . As the diagonals are not equal and the sides are equal, the given quadrilateral is a Rhombus.
Properties of a square
A. All 4 sides are equal
B. Opposite angles are equal and supplementary
C. Diagonals are equal and bisect each other at right angles
Properties of a Rhombus
A. All 4 sides are equal
B. Opposite angles are equal but not supplementary
C. Diagonals are not equal but bisect each other at right angles.
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