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Two triangles on the same base and between the same parallels are equal in area ... please prove this

Posted by Kessang Tamang Kessang Tamang 5 years, 2 months ago

CBSE > Class 09 > Mathematics

1 answers

Gaurav Seth 5 years, 2 months ago

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

Given
: Two triangles ABC and DBC are on the same base BC and between same parallels EF and BC.

To Prove : ar(ΔABC) = ar(ΔDBC)

Construction : Through B, draw BE || AC intersecting line AD in E and through C draw CF || BD intersecting the line DA in F.

Proof : EACB and DFCB are parallelograms (Since two pairs of opposite sides are parallel)

Also ||gm EACB and ||gm DFCB are on the same base BC and between same parallels EF and BC.
∴ ar(||gm EACB)= ar(||gm DFCB)...(i)
Now AB is the diagonal of ||gm EACB
∴ ar(ΔEAB) = ar(ΔABC)
∴ ar(ΔABC) = (1/2)ar(||gm EACB) .....(ii)
Similarly,
ar(ΔDBC) = (1/2) ar(||gm DFCB)...(iii)
From equations (i), (ii) and (iii), we get
ar(Δ ABC) = ar(Δ DBC)

0Thank You

ANSWER

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CBSE > Class 09 > Mathematics