Question

6. Given: PQ and QR are mid segments of A ABC and
AB = BC
A
P,
C
B
R
Fig. 11.79
Prove: BPQR is a rhombus.
​

Answer 1

Answer:

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∥

2

1

BC

⇒PQ=BR

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

3. QR∥AB

Reason- R is mid-point of BC

4. QR=

2

1

AB

⇒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.