If cosines of two angles of a triangle are proportional to the opposite sides, show that the triangle is isosceles

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.

If two sides and the median drawn to one of these two sides of a trlangle are proportional to the corresponding sides and median of another triangle,prove that the two triangles are similar.

In triangle ABC, a sin A= b sin B. Show that the triangle is isosceles.

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

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the bisectors of the corresponding angles of the triangles. [The end-points of the angular bisectors are on the opposite sides of the angles.]

Sides of a triangle are 4, 5, 6 cms. Show that the greatest angle is twice the smallest angle.

The sides of a right angled triangle are in G.P.Find the common ratio.

If one angle of a triangle is equal to one angle of another triangle and the bisectors of these equal angles divide the opposite side in the same ratio then show that the triangle are similar.

prove by using the principle of similar triangles that: if a line segment divides two sides of a triangle proportionally, then it is a parallel to the third side.

The measures of the angles of a triangle are in A.P. If the greatest angle is double the least angle, express the angles of the triangle in degree and radian.