Triangle and Quadrilateral

Unit: 10

Book Icon Class 10: Mathematics

Triangle and Quadrilateral, Theorems on Area of Triangle and Quadrilateral

Triangle: A triangle is a closed shape with three sides and three angles. The sum of its three angles is always 180 degrees.

Quadrilateral: A quadrilateral is a closed shape with four sides and four angles. The sum of its four angles is always 360 degrees.

Theorem 1: Parallelograms on the same base and between the same parallel lines are equal in area.

Theorem 2: The area of a triangle is equal to half the area of a parallelogram on the same base and between the same parallel lines.

Theorem 3: Triangles on the same base and between the same parallel lines are equal in area.

Test your knowledge

Attempt these questions independently to reinforce your learning:

Q1.

In a figure, parallelograms FGHE and FGIJ are standing on the same base FG, where, FE || GH, EI || FG and FJ || GI. [SEE 2080 SP]

a. Are the area of parallelograms FGHE and FGIJ same? [1K]
b. Prove that: Area of \(\triangle EFJ\) = Area of \(\triangle HGI\). [2U]
c. When the parallelogram EFGH is made as a rectangle lying on the same base FG, will it make any change in the area? Write with reason. [1HA]