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If a parallelogram and a triangle …

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If a parallelogram and a triangle are on the common base and between the same parallels,then prove that the area of the triangle is equal to half the area of the parallelogram.

Posted by Rahul Kumar 5 years, 4 months ago

CBSE > Class 09 > Mathematics

1 answers

Jayavel Arumugam 5 years, 4 months ago

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)]

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