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Geometry: Proportionality Theorem
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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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