Question

P,Q & R are the midpoints of BC,CA and AB respectively. prove that ar(PQR) = 1/4 ar(ABC)
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Answer 1

Step-by-step explanation:

ar(ABC) = ar(RBP)+ar(AQR)+ar(PQC)+ar(PQR)

now, we should prove that ∆PQR≈∆PBR

so, BP= RQ ( opp.side in ∆)

RP ( common side )

/_BPQ=/_BRQ ( opp. angles )

therefore , according to SAS congruency ∆PQR≈∆PBR ... ( do this method for all ∆s)

finally,

ar(ABC) = ar(RBP)+ar(AQR)+ar(PQC)+ar(PQR)

ar(ABC) = 4ar(PQR)

1/4ar(ABC) = at(PQR)....hence proved ..:)