a line parallel to one side of a triangle divides the other two sides in equal proportion
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Given: In a △PQR, line l∥ side QR, line l intersect the sides PQ and PR in two distinct points M and N respectively.
To prove: MQPM=NRPN ... (i)
Construction: segQN and segRM are drawn.
Proof: A(△QMN)A(△PMN)=MQPM
(Both triangles have equal height with common vertex M)
∴A(△RMN)A(△PMN)=NRPN ... (ii)
But A(△QMN)=A(△RMN), because they are between parallel lines MN and QR and have equal height corresponding to their common base MN ..... (iii)
From (i), (ii) and (iii), we get
A(△QMN)A(△PMN)=A(△RMN)A(△PMN)
∴MQPM=NRPN [hence proved]
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