M and N are the points on sides QR and PQ respectively of a `trianglePQR`, right angled at Q. prove that ` PM^(2) + RN^(2)= PR^(2)+MN^(2)`

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

M and N are the mid-points of the sides QR and PQ respectively of a DeltaPQR , right-angled at Q. Prove that : (i) PM^(2)+RN^(2)=5MN^(2) (ii) 4PM^(2)=4PQ^(2)+QR^(2) (iii) 4RN^(2)=PQ^(2)+4QR^(2) (iv) 4(PM^(2)+RN^(2))=5PR^(2)

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) .

P and Q are points on the sides CA and CB respectively of ABC, right angled at C. Prove that AQ^(2)+BP^(2)=AB^(2)+PQ^(2)

P and Q are points on the sides CA and CB of a ∆ABC , right angled at C. Prove that AQ^2 + BP^2 = AB^2 + PQ^2 .

M and N are points on the sides PQ and PR respectively of anglePQR . If PQ = 1.28 PR = 2.56, PM = 0.16 and PN = 0.32, prove that MN || QR.

PQR is a triangle whose /_Q is right angle. If S is any point on QR, then prove that PS^(2) + QR^(2) =PR^(2) + QS^(2)

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 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