Given: P,Q,R are mid-points of AB, AC, BC.
To prove: BRQP is parallelogram.
Proof:
Statement
1. PQ∥BC
Reason-Mid-point theorem as P,Q are mid-points
2. PQ∥12BC
⇒PQ=BR
Reason: mid-point theorem as P,Q are mid-points
3. QR∥AB
Reason- R is mid-point of BC
4. QR=12AB
⇒QR=PB
Reason: mid-point theorem as Q,R are mid-points
P is mid-point of AB
5. BRQP is parallelogram
Reason: pairs of opposite sides are parallel and equal.
Hence proved.