Question

Given: Area of parallelogram = Base $\times$ Height

Statement 1: A diagonal of a parallelogram divides it into two congruent triangles.

Statement 2: Areas of two congruent triangles are exactly equal.

Chose the correct option.

• A. Both the statements are true and enough to determine area of a triangle
• B. Both the statements are true but not enough to determine area of a triangle
• C. Statement 1 is true and Statement 1 is false
• D. Statement 1 is false and Statement 2 is true

Answer 1

The correct option is A

Both the statements are true and enough to determine area of a triangle

Area of parallelogram = Base × Height.

In ∆ABD and ∆CDB,

AB = CD (Opposite sides of a parallelogram)

AD = BC (Opposite sides of a parallelogram)

BD = DB (Common)

∆ABD ≅ ∆CDB [By SSS congruence condition]

So, statement 1 is true.

Also, two figures are said to be congruent if they have exactly same shape and size. This means that they have equal area. Hence, two congruent triangles will have equal areas but the converse may not be true. Statement 2 is also correct.

From the two statements, we can say that

Area (∆ABD) + Area (∆CDB) = Area (parallelogram ABCD)

2 × Area (∆ABD) = Base × Height

Area (∆ABD) = $\frac{1}{2}$ × Base × Height.

Hence, both the statements are correct and enough to determine the area of a triangle.