# In the triangle Δ

The figure according to given information is as shown below

Consider ΔAQS and ΔBQC

QS = QC … given

SQA = CQB … vertically opposite angles

AQ = BQ … CQ is median on AB

Therefore, ΔAQS ΔBQC … SAS test for congruency

ASQ = BCQ … corresponding angles of congruent triangles

Thus AS || BC because ASQ and BCQ are pair of alternate interior angles with transversal as CS

AS || BC … (i)

Consider ΔAR and ΔCPB

BP = PR … given

APR = BPC … vertically opposite angles

AP = CP … BP is median on AC

Therefore, ΔAPR ΔCPB … SAS test for congruency

ARP = CBP … corresponding angles of congruent triangles

Thus AR || BC because ARP and CBP are pair of alternate interior angles with transversal as BR

AR || BC … (ii)

From (i) and (ii) we can say that

AS || AR

But point A lies on both the lines AS and AR which means AS and AR are on the same straight line

Thus, point A, S and R are collinear points

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In the triangle ΔWest Bengal Mathematics