1.

If S is a point on side PQ of a `DeltaPQR` such that PS=QS=RS, thenA. `PRcdotQR=RS^(2)`B. `QS^(2)+RS^(2)=QR^(2)`C. `PR^(2)+QR^(2)=PQ^(2)`D. `PS^(2)+RS^(2)=PR^(2)`

Answer» Given , in `DeltaPQR`,
PS=QS=RS ….(i)
In `DeltaPSR`, PS=RS [fromEq. (i)]
`rArr angle1=angle2` ….(ii)
Similarly, in `DeltaRSQ`,
`rArr angle3=angle4` ….(iii)
[corresponding angles of equal sides are equal]
Now, in `DeltaPQR`, sum of angles=`180^(@)`
`rArr angle P+angleQ+angleR=180^(@)`
`rArrangle2+angle4+angle1+angle3=180^(@)`
`rArrangle1+angle3+angle1+angle3=180^(@)`
`rArr2(angle1+angle3)=180^(@)`
`rarrangle1+angle3=(180^(@))/2=90^(@)`
`therefore angleR=90^(@)`
In `DeltaPQR`, by Pythagoras theorem,
`PR^(2)+QR^(2)=PQ^(2)`


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