PQRS is a trapezium with PQ || SR. If M and N are two points on the non-parallel sides PS and QR respectively, such…

CBSE Class 10 Maths PYQ · Triangles · Similarity with Quadrilaterals · 2 Marks · March 2024 · Standard

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1302 Marks · March 2024 · Standard

PQRS is a trapezium with PQ $||$ SR. If M and N are two points on the non-parallel sides PS and QR respectively, such that MN is parallel to PQ, then show that $\frac{PM}{MS} = \frac{QN}{NR}$.

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Join PR
PQ $||$ SR and MN $||$ PQ $\Rightarrow$ MN $||$ SR
In $\triangle PSR$,
$\frac{PM}{MS} = \frac{PO}{OR}$ ... (i)
In $\triangle PQR$,
$\frac{PO}{OR} = \frac{QN}{NR}$ ... (ii)
From (i) and (ii), $\frac{PM}{MS} = \frac{QN}{NR}$