__CHAPTER 9 AREAS OF PARALLELOGRAMS AND TRIANGLES__

- Area of a figure is a number (in some unit) associated with the part of the plane enclosed by that figure.

- Two congruent figures have equal areas but the converse need not be true.

- If a planar region formed by a figure T is made up of two non-overlapping planar regions formed by figures P and Q, then area (T) = area (P) + area(Q), where area (X) denotes the area of figure X.

- Two figures are said to be on the same base and between the same parallels, if they have a common base (side) and the vertices, (or the vertex) opposite to the common base of each figure lie on a line parallel to the base.

- Parallelograms on the same base (or equal bases) and between the same parallels are equal in area.

- Area of a parallelogram is the product of its base and the corresponding altitude.

- Parallelograms on the same base (or equal bases) and having equal areas lie between the same parallels.

- If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.

- Triangles on the same base (or equal bases) and between the same parallels are equal in area.

- Area of a triangle is half the product of its base and the corresponding altitude.

- Triangles on the same base (or equal bases) and having equal areas lie between the same parallels.

- A median of a triangle divides it into two triangles of equal areas.