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The GMAT Math practice question is a problem on polygons and their shapes in geometry

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?

1. Square
2. Rectangle but not a square
3. Rhombus
4. Parallelogram but not a rhombus
5. Kite

The correct choice is (C) and the correct answer is Rhombus.

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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