In `/_\PQR`, the line segment PS is perpendicular to QR and `PS^2=QS×RS`. Show that the triangle is a right angled one.

The length of the sides of a triangle are a+b , ab-1 and sqrt((a^2+1)(b^2+1)) . Show that it is a right angled triangle.

the two triangles formed by drawing perpendicular from right angle to the hypotenuse of a right angled triangle are similar and both of them are similar to the original triangle.

If cot (A/2)=(b+c)/a.show that /_\ABC is right angled.

If cosines of two angles of a triangle are inversely proportional to the opposite sides, show that the triangle is either isosceles or right-angled.

The length of the sides of a triangle are ax-by , ay+bx and sqrt((a^2+b^2)(x^2+y^2)) . Show that it is a right angled triangle.

In the triangle ABC, BC+CA=m^2+2mn-n^2 , CA+AB=(m+n)^2 and AB+BC=2m^2 . Show that it is a right angled triangle.

If in triangle ABC , (a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B) ,show that the triangle is either'isosceles or right angled.

In the triangle ABC, BC = m^2 -n^2 , AC =3 mn and AB = m^2+n^2 . Prove that it is a right angled triangle.

If sin^2A + sin^2B= sin^2 C ,show that /_\ABC is right-angled.

In the triangle ABC,AB=p^2-q^2,BC=p^2+q^2 and CA=2pq then prove that triangleABC is right angled.Which of the angles of the triangle is right angle?