Geometry: Proportionality Theorem

 Similar Triangles: Proportionality Theorem Theorem: If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
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Example In fig, if PS/SR = QT/TR and RST = RTS, prove that RPQ is isosceles.
Solution : In PQR, We have
 PS/SR = QT/TR .... [Given] Therefore, by the converse of basic proportionality theorem, ST PQ RST = RPQ and RTS = RQP                                               [Corresponding angles] But, RST = RTS .....[Given]RPQ = RQP P = Q QR = PR ....[Sides opposite to equal angles are equal] RPQ is isosceles.

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