Sides, Angles and diagonals of a quadrilateral; Different types of quadrilaterals: Trapezium, parallelogram, rectangle, rhombus and square.
• Sum of the angles of a quadrilateral is 360º,
• A diagonal of a parallelogram divides it into two congruent triangles,
• In a parallelogram
(i) opposite angles are equal
(ii) opposite sides are equal
(iii) diagonals bisect each other.
• A quadrilateral is a parallelogram, if
(i) its opposite angles are equal
(ii) its opposite sides are equal
(iii) its diagonals bisect each other
(iv) a pair of opposite sides is equal and parallel.
• Diagonals of a rectangle bisect each other and are equal and vice-versa
• Diagonals of a rhombus bisect each other at right angles and vice-versa
• Diagonals of a square bisect each other at right angles and are equal and vice-versa
• The line-segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it
A line drawn through the mid-point of a side of a triangle parallel to another side bisects the third side,
• The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, taken in order, is a parallelogram.