# Coordinate Geometry : Quadrilateral Properties

This aptitude practice question is a coordinate geometry question. This one is a medium level difficulty question and tests the following concepts: finding length of a line segment given coordinates of its end points; properties of quadrilaterals including square, rectangle, rhombus and parallelogram.

## 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?

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

• #### 1. Properties of a square

1. All 4 sides are equal. Opposite sides are parallel.
2. All angles are equal.
3. Opposite angles are equal and supplementary (sum of the angles equals 180o)
4. Diagonals are equal and bisect each other at right angles
5. A square is a cyclic quadrilateral

#### 2. Properties of a Rectangle

1. Opposite sides are parallel and equal.
2. All angles are equal.
3. Opposite angles are equal and supplementary
4. Diagonals are equal and bisect each other but NOT at right angles
5. A rectangle is a cyclic quadrilateral

#### 3. Properties of a Parallelogram

1. Opposite sides are parallel and equal.
2. Opposite angles are equal
4. Diagonals are NOT equal but bisect each other but NOT at right angles
5. A parallelogram is NOT a cyclic quadrilateral

#### 4. Properties of a Rhombus

1. Opposite sides are parallel and equal.
2. All 4 sides are equal.
3. Opposite angles are equal
5. Diagonals are NOT equal but bisect each other at right angles
6. A rhombus is NOT a cyclic quadrilateral

## Online TANCET MBA CourseTry it Free!

Register in 2 easy steps and start learning in 5 minutes!