Area Theorems

Theorem 1:

► Parallelogram on the same base and between the same parallels is equal in area.

Theorem 2:

► The area of a parallelogram is equal to that of a rectangle on the same base and of the same altitude, i.e., between the same parallel lines.

Theorem 3:

► The area of a triangle is half of the area of a parallelogram on the same base and between the same parallels.

Theorem 4:

► Triangles between the same base and between the same parallels are equal in area.

Theorem 5:

► Triangles with equal areas on the same base have equal corresponding altitudes.

► If a triangle and a parallelogram are on the same base and between the same parallel lines, the area of the triangle is equal to half of the parallelogram.

area of ΔAPD = (1/2) area of ΔABCD

► Triangles having equal areas and having one side of the triangles equal to one side of the other have their corresponding altitudes equal.

► A median of a triangle divides it in two triangles of equal areas.

► The line segment joining the mid-points of a pair of opposite sides of a parallelogram divides it into two equal parallelograms.