If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles.

If two medians of a triangle are equal , prove analytically that the triangle is isosceles .

BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

Prove that the area of a right-angled triangle of a given hypotenuse is maximum when the triangle is isosceles.

If the bisector of angle A of triangle ABC makes an angle theta with BC, then sin theta is

The base of an isosceles triangle measures 4 units base angle is equal to 45^(@) . A straight line cuts the extension of the base at a point M at the angle theta and bisects the lateral side of the triangle which is nearest to M. The area of quadrilateral which the straight line cuts off from the given triangle is

If the cotangents of half the angles of a triangle are in A.P., then prove that the sides are in A.P.

The internal and external bisectors of the vertical angle of a triangle intersect the circumcircle of the triangle at the points P and Q. Prove that PQ is a diameter of the circle.

If the angles of a triangle are in ratio 1 : 1 : 2, then the ratio of the sides of the triangle is

If the sides of right angled triangle are in G.P then the cosines of the acute angle of the triangle are-

Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2 < c^2, then prove that triangle is obtuse angled .