In Fig.9.29, ar(DRC) = ar(DPC) and ar(BDP) = ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.
Answer
Given,
ar(DRC) = ar(DPC) and 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). Therefore, they must lying between the same parallel lines.
Thus, AB ∥ CD
Therefore, ABCD is a trapezium.
also,
ar(DRC) = ar(DPC). Therefore, they must lying between the same parallel lines.
Thus, DC ∥ PR
Therefore, DCPR is a trapezium.
