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.