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If S is the mid-point of side QR of a De...

If S is the mid-point of side QR of a `DeltaPQR`, then prove that `PQ+PR=2PS`.

Text Solution

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Clearly, by triangle law of addition, we have

`PQ+QS=PS` . . . (i)
and `PR+RS=PS` . . . (ii)
On adding Eqs. (i) and (ii), we get
`(PQ+QS)+(PR+RS)=2PS`
`implies(PQ+PR)+(QS+RS)=2PS`
`impliesPQ+PR+0=2PS`
[`because` S is mid-point of `QR thereforeQS=-RS`]
Hnce, PQ+PR=2PS Hence, proved.
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