Home
Class 12
MATHS
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

Verified by Experts

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.
Promotional Banner

Similar Questions

Explore conceptually related problems

In the given figure, PS in the bisector of /_QPR " of "DeltaPQR . Prove that (QS)/(SR)= (PQ)/(PR) .

S and T are points on sides PR and QR of DeltaPQR such that /_P= /_RTS . Show that DeltaRPQ ~ DeltaRTS .

In the following figures, PQ = LM, Q is the midpoint of PR and M is the midpoint of LN. Using the axioms, prove that PR = LN.

In the given figure, the side QR of DeltaPQR is produced to a point S. If the bisectors of anglePQR and anglePRS meet at point T, then prove that angleQTR=(1)/(2)angleQPR .

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

D, E and F are respectively the mid-points of sides AB, BC and CA of DeltaABC . Find the ratio of the areas of DeltaDEF" and "DeltaABC .

Point S lies in the interior of A PQR. Prove that, SQ + SR lt PQ + PR.

In the given figure, CM and RN are respectively the medians of DeltaABC and DeltaPQR . If DeltaABC ~DeltaPQR , prove that, (CM)/(RN)=(AB)/(PQ)

In the given figure, sides QP and RQ of DeltaPQR are produced to points S and T respectively. If angleSPR=135^(@) and anglePQT=110^(@) , find anglePRQ .

The line segment joining the mid-points of any two sides of a triangle in parallel to the third side and equal to half of it.