Every Diagonal of a Parallelogram Divides it into Two Triangles of Equal Area Theorem & Proof

The statement “Every Diagonal of a Parallelogram Divides it into Two Triangles of Equal Area” is a property related to the area of the triangle and area of a parallelogram. By using the Every Diagonal of a Parallelogram Divides it into Two Triangles of Equal Area theorem the students of 9th grade can solve different types of problems related to the concept Area.

Every Diagonal of a Parallelogram Divides it into Two Triangles of Equal Area – Theorem

Statement:
Prove that Every Diagonal of a Parallelogram Divides it into Two Triangles of Equal Area.
Proof:
Here ABCD is a parallelogram and BD is diagonal

In ∆ADB and ∆CBD
∠ADB = ∠CBD( alternate angles )
Also AB // DC
∠ABD = ∠CDB( alternate angles )
DB = BD
Therefore ∆ADB ≅ ∆CDB( by SAS congruence rule)
Since congruent figures have the same area
Hence proved.

FAQs on A Diagonal Divides a Parallelogram into Two Triangles of Equal Area

1. What divides a parallelogram into two triangles of equal area?

The diagonal divides a parallelogram into two triangles of equal area.

2. Are the opposite sides of a parallelogram always equal?

opposite sides of a parallelogram are equal. The diagonals of a parallelogram bisect each other. Each diagonal of a parallelogram bisects into two congruent triangles.The quadrilateral is a parallelogram.

3. Do all parallelograms have 4 equal sides?

A parallelogram has two parallel pairs of opposite sides. A rectangle has two pairs of opposite sides parallel, and it has four right angles. It is also a parallelogram and it has two pairs of parallel sides. A square has two pairs of parallel sides, four right angles, and all four sides are equal.