in the figure the lines AP and BR are parallel. The distance between them is 3 cm and BC = EF= QR = 4 cm
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Given: In ∆ABC, P is the mid point of BC. PQ||CA, PQ meets AB in Q. QR||BC, QR meets AP in R.
To prove: 1. AP = 2 AR
2. BC = 4 QR
Proof:
In ∆ABC, P is the mid point of BC and PQ||AB.
∴ Q is the mid point of AB (Converse of mid-point theorem)
In ∴ ABP, Q is the mid point of AB and QR||BP.
∴ R is the mid point of AP. (Converse of mid point theorem)
⇒ AP = 2AR
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