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Areas of Parallelograms and Triangles
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17/07/2021 11:25 am
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In Figure, ar(DRC) = ar(DPC) and ar(BDP) = ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.
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17/07/2021 11:26 am
Given,
ar(△DRC) = ar(△DPC)
ar(△BDP) = ar(△ARC)
To Prove,
ABCD and DCPR are trapeziums.
Proof:
ar(△BDP) = ar(△ARC)
⇒ ar(△BDP) – ar(△DPC) = ar(△DRC)
⇒ ar(△BDC) = ar(△ADC)
ar(△BDC) = ar(△ADC).
∴ ar(△BDC) and ar(△ADC) are lying in-between the same parallel lines.
∴ AB ∥ CD
ABCD is a trapezium.
Similarly,
ar(△DRC) = ar(△DPC).
∴, ar(△DRC) andar(△DPC) are lying in-between the same parallel lines.
∴ DC ∥ PR
∴ DCPR is a trapezium.