Question

Two triangles​have same Base and between same parallels are equal in area

Answer 1

Yes they are equal in area

Answer 2

Let ∆ABC and ∆ABD be on the same base AB and between the same parallel AB and CD. It is require to prove that ∆ABC = ∆ABD.

Construction: A parallelogram ABPQ is constructed with AB as base and lying between the same parallels AB and CD.

Triangles on Same Base and between Same Parallels




Proof: Since ∆ABC and parallelogram ABPQ are on the same base AB and between the same parallels AB and Q,

Therefore, ∆ABC = ½(Parallelogram ABPQ)

Similarly, ∆ABD = ½(Parallelogram ABPQ)

Therefore, ∆ABC = ∆ABD.

Note: Since the relationship between the areas of a triangle and a parallelogram on the same base and between the same parallels in known to us, so that parallelogram ABPQ is constructed]