**Important Concepts and Formulas**

1. The sum of the angles of a
quadrilateral is 360°.

2.

**Properties of a parallelogram:**

i.
A
diagonal of a parallelogram divides it into two congruent triangles.

ii.
The
opposite sides of a parallelogram are equal.

iii.
The
opposite angles of a parallelogram are equal.

iv.
The
diagonals of a parallelogram bisect each other.

3. A quadrilateral is a parallelogram,
if its

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 parallel and equal.

4. The diagonals of a rectangle bisect
each other and are equal.

5. If the diagonals of a parallelogram
are equal, then it is a rectangle.

6. The diagonals of a rhombus bisect
each other at right angles.

7. If the diagonals of a parallelogram bisect
each other at right angles, then it is a rhombus.

8. The diagonals of a square bisect each
other at right angles and are equal.

9. If the diagonals of a parallelogram
bisect each other at right angles and are equal, then it is a square.

10. The quadrilateral formed by joining
the mid-point of the sides of a quadrilateral, in order, is a parallelogram.

11.

**Mid-point Theorem:**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.
12.

**Converse of Mid-point Theorem:**The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.