Question

(33) Prove that, Two triangles on the same base and between
the same parallels are equal in area.​

Answer 1

Step-by-step explanation:

Proof: △ABC & △ABD are drawn on the same base AB as base lying between the same two parallel lines L

1

& L

2

.

Here we will be using the following property of a triangle and parallelogram drawn on the same base between two parallel lines.

Since △ABC & ∣∣gm ABPQ are on the same base and between the same parallel L

1

& L

2

.

∴ar(△ABC)=

2

1

area of parallelogram ABPQ.

Similarly,

ar(△ABD)=

2

1

area of parallelogram ABPQ.

∴ area of △ABC=area of △ABD.