In `DeltaPQR,` set `XY||` sides QR, M and N are midpoints of seg PY and seg PR respectively. Prove that:
(i) `DeltaPXM~DeltaPQN` (ii) `"seg"XM||"sec"QN`.

In DeltaPQR , seg XY|| side QR . M and N are the midpoints of seg PY and side PR respectively, P-M-Y-N-R . Prove that (i) DeltaPXM~DeltaPQN (ii) seg XM|| seg QN .

In A PQR, if PQ=PQ and L,M and N are the mid-points of the sides PQ,PR and RP respectively.Prove that LN=MN

In the figure, M and N are the midpoints of sides PQ and PR respectively . If MN =6 cm then find QR. State your reason .

In DeltaPQR, /_Q= 90^(@) . Equilateral triangles APQ, BQR and CPR are described on sides PQ, QR and PR respectively. Prove that ar(APQ)+ar (BQR)= ar(CPR) .

M and N are mid- point on sides QR and PQ respectively of /_\ PQR , right-anggled at Q. Prove that : PM^(2)+RN^(2)= 5 MN^(2) .

M and N are mid point on sides QR and PQ respectively of /_\ PQR , right-anggled at Q. Prove that : 4PM^(2)= 4PQ^(2)+QR^(2) .

In the adjoining figure , seg PQ || AB. Seg PR || seg BD. Prove that QR||AD.

In DeltaPQR seg PM is a median. Angle bisectors of /_PMQ and /_PMR interesect side PQ and side PR in points X and Y respectively. Prove that XY||QR .

In DeltaPQR seg PM is a median. Angle bisectors of /_PMQ and /_PMR interesect side PQ and side PR in points X and Y respectively. Prove that XY||QR . Complete the proof byfilling in the boxes:

In the given figure, points S,T and U are the midpoints of sides PQ,QR and PR respectively. IF PV bot QR, then prove that square SVTU is a cyclic quadrilateral.