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

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 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 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)

S and T are points on the sides PQ and PR, respectively of Delta PQR , such that PT = 2 cm, TR = 4 cm and ST is parallel to QR. Find the ratio of the areas of Delta PST and Delta PQR .

In a triangle PQR, L and M are two points on the base QR, such that /_LPQ = /_QRP and /_RPM = /_RQP . Prove that: PQ^2 = QR xx QL

In figure A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

ABCD is a square. P, Q and Rare the points on AB, BC and CD respectively, such that AP = BQ = CR. Prove that: PQ = QR

In the adjoining figure, QX and RX are the bisectors of the angles Q and R respectively of the triangle PQR. If XS bot QR and XT bot PQ , prove that : Delta XTQ ~= Delta XSQ

In the adjoining figure, DeltaPQR is formed by the sides PQ, QR and RP which are drawn parallel to sides AB,BC and CA respectively of DeltaABC. Prove that " "PQ+QR+RP=2(AB+BC+CA).