Question

Prove that:
Triangles on the same base and between the same parallels are equal in area.

Answer 1

To prove: Triangles on the same and between same parallel is equal in are.

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 $L_1$ & $L_2$.

$\therefore ar\left(△ABC\right)=\frac{1}{2}$ area of parallelogram $ABPQ$.

Similarly,

$ar\left(△ABD\right)=\frac{1}{2}$ area of parallelogram $ABPQ$.

$\therefore$ area of $△ABC=$area of $△ABD$.