Question

In the figure, PQRS is a trapezium in which $PQ \parallel SR$. There are points E and F respectively such that EF intersects SQ at G. Prove that $EQ 	imes GS = GQ 	imes FS$.

Accepted Answer

In $	riangle EGQ$ and $	riangle FGS$: $\angle EGQ = \angle FGS$ (vertically opposite angles). $\angle EQG = \angle FSG$ (alternate interior angles as $PQ \parallel SR$). By AA similarity criterion, $	riangle EGQ \sim 	riangle FGS$. So $\frac{EQ}{FS} = \frac{GQ}{GS} \implies EQ 	imes GS = GQ 	imes FS$.

Similar triangles in trapezium

Explanation

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