Math, asked by mathew5883, 4 months ago


19. Prove that "The area of a triangle is half the area of a parallelogram if they both have the same base und lie between the same pair of parallel lines"​

Answers

Answered by sm190026m
0

Answer:

Let ΔABP and a parallelogram ABCD be on the same base AB and between the same parallels AB and PC.

To Prove : ar( ΔPAB ) = (1/2)ar( ABCD)

Draw BQ ||AP to obtain another parallelogram.ABQP and ABCD are on the same base AB and between the same parallels AB and PC.

There fore, ar(ABQP) =  ar(ABCD)

But ΔPAB ≅ ΔBQP( Diagonals PB divides parallelogram ABQP into two congruent triangles.

So  ar (PAB) = ar(BQP) -----------(2)

∴ ar (PAB) = (1/2)ar(ABQP) -----------------(3) [ from (2)]

This gives ar (PAB) = (1/2)ar(ABCD)   [ from (1) and (3)]

Step-by-step explanation:

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