PQR is a triangle right angled at P and M is a point on QR such that PM `bot` QR . Show that `PM^(2)` = QM .MR.

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 a triangle PQR, anglePQR = 90^@ S is any point onQR. Prove that PS^2+QR^2 = PR^2+QS^2 .

If a point Q lies between two points P and R such that PQ = QR, prove that PQ = 1/2 PR.

If ABC is a right triangle right-angled at B and M, N are the midpoints of AB and BC respectively. Then 4 (AN^2 + CM^2) =

In the given figure ABC is a right triangle and right angled at B such that /_BCA = 2/_BAC. Show that hypotenuse AC = 2BC.

In a right angled traingle PQR , angleP is right angle and PS is perpendicular to the hypetnuse QR. Prove that 1/(PS^2)-1/(PQ^2)=1/(PR^2)

Draw a triangle PQR , such that PQ = 6cm, QR= 5cm, and PR = 6 cm.

triangleABC is a right triangle right angled at A and AD bot BC . Then BD/DC is equal___

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

(i) If the cosines of two of the angles of a triangle, which is not isosceles, are iversely proportional to the corresponding opposite sides, show that the triangle is right angled. (ii) In a triangle ABC, If A=2B then show that, a^(2)- b^(2)=bc .