A quadrilateral has four sides, vertices and angles. The sum of four angles in a quadrilateral is always 360°. Types of quadrilaterals are trapezium, parallelogram, rectangle, rhombus, square and kite.
Properties of a parallelogram:
1. A diagonal of a parallelogram divides it into two congruent triangles.
2. Opposite sides of a parallelogram are equal.
3. Opposite angles of a parallelogram are equal.
4. Diagonals of a parallelogram bisect each other.
A quadrilateral is a parallelogram, if:
1. each pair of opposite sides of a quadrilateral is equal.
2. each pair of opposite angles of a quadrilateral is equal.
3. the diagonals of a quadrilateral bisect each other.
4. the pair of opposite sides is equal and parallel.
Properties of a rectangle:
1. The opposite sides of a rectangle are equal and parallel.
2. The measure of each angle in a rectangle is 90°.
3. Diagonals of a rectangle bisect each other and are equal.
Properties of a square:
1. All sides of a square are equal.
2. Opposite sides of a square are parallel.
3. Each angle of a square is equal to 90°.
4. Diagonals of a square bisect each other and are equal.
Properties of a rhombus:
1. All four sides of a rhombus are equal.
2. The pair of opposite sides are parallel.
3. The diagonals of a rhombus bisect each other and are perpendicular.
4. The pair of adjacent angles are supplementary.
Properties of a trapezium:
1. One pair of opposite sides is parallel.
Properties of a kite:
1. Two pairs of distinct adjacent sides are equal.
2. Diagonals of a kite are perpendicular.
A line segment joining the mid-points of two sides of a triangle is parallel to the third side.
A line drawn through the mid-point of one side of a triangle, parallel to another side, bisects the third side.