Sum of the
angles of a quadrilateral is 360°. A diagonal of a parallelogram divides it into two congruent triangles.
In a parallelogram,
- opposite sides are equal
- opposite angles are equal
- diagonals bisect each other
A quadrilateral is a parallelogram, if (i) opposite sides are equal or (ii) opposite angles are equal or (iii) diagonals bisect each other or (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 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, in order, is a parallelogram.