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You are here: Home » GMAT Test Prep Questions » Geometry » Question 1
Data Sufficiency   GMAT Problem Solving : Geometry, Quadrilaterals
The GMAT Math practice question is a problem on polygons and their shapes in geometry

Question 1
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.

Explanatory Answer
The lengths of the four sides, AB, BC, CD and DA are all equal to under root 41.

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 under root 162 and the length of BD is under root 2.

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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