The areas of two similar triangles are in the ratio of the square of the corresponding medians.
Solution : Given : \(\triangle\) ABC ~ \(\triangle\) DEF and AP, DQ are their medians. To Prove : \(area(\triangle ABC)\over area(\triangle DEF)\) = \({AP}^2\over {DQ}^2\) Proof : Since the ratio of the area of two similar triangles is equal to the ratio of the squares of any two corresponding sides. \(\therefore\) \(area (\triangle ABC)\over area …