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In the figure 2.28 seg PS is themedian of Δ PCR and P1. I OR.Prove that,QRQRFig. 2.284In Δ ABC, point M is the m |
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Answer» 1. In figure PS is the median Triangle PTS is a right angled triangle. Therefore according to figure angle PTS is a right angle. Therefore both the anlge that is angle TPS and angle TSP are not right angles but both of them are acute angles. Therefore if angle TSP is acute then angle PSR has to be an obtuse angle.Consider triangle PTRangle PSR is an obtuse angle which I already proved.There is a theorem which states relation between side opposite to obtuse angle with two remaining sides. According to that theorem PR^2 = SR^2 + PS^2 + 2SR*STIt can be rewritten as PR^2 = PS^2 + QR*ST + (QR/2)^2SR^2 is rewritten as (QR/2)^2 and 2SR is rewritten as QR Hence, proved. |
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