Question

X. P and Q are mid-points of the sides AB and AC of a triangle ABC. PQ
that PQ = QR. Prove that PRCB is a parallelogram.
ngle ABC. PQ is produced to R such​

Answer 1

Step-by-step explanation:

In triangle APQ and triangle ABC angle A is common and angle APQ is equal to angle ABC thus by similarity we get PQ/BC is equal to 1/2 thus PR being 2*PQ is equal to BC thus it is a parallelogram

Answer 2

Step-by-step explanation:

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.