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Question

In ΔPQR are the mid points of side AB, BC and AC respectively. PQ and QR are joined. Prove that BRQP is a parallelogram.
1078337_83ebd3cf404345249a4ba4e256d120e7.png

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Solution

Given: P,Q,R are mid-points of AB, AC, BC.

To prove: BRQP is parallelogram.

Proof:

Statement

1. PQBC

Reason-Mid-point theorem as P,Q are mid-points

2. PQ12BC

PQ=BR

Reason: mid-point theorem as P,Q are mid-points

3. QRAB

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.


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