Mathematics

Problem

(a) State the Basic Proportionality Theorem. (b) In a triangle

PQR

, points

S

PQ

and

T

PR

are chosen such that

\dfrac{PS}{SQ}=\dfrac{PT}{TR}

. Prove that

ST\,\parallel\,QR

. (c) If

PS:SQ = 1:3

, find the ratio of the areas of

\triangle PST

and

\triangle PQR