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Sides AB and BC and median AD of a trian...

Sides AB and BC and median AD of a triangle ABC are respectively propor-/ tional to sides PQ and QR and median PM of `DeltaPQR` (see Fig. 6.41). Show that `DeltaABC~DeltaPOR`.

Text Solution

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We can draw the figure as per the details given. Please refer to video for figure.
In this question, we are given,
`(AB)/(PQ) = (BC)/(QR) = (AD)/(PM)->Eq(1)`
Bow, as AD and PM are medians, we can says that
` BC = 2BD and QR = 2QM`
Putting it in Eq(1)
`(AB)/(PQ) = (2BD)/(2QM) = (AD)/(PM)`
`(AB)/(PQ) = (BD)/(QM) = (AD)/(PM)`
...
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