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

Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angle triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides.

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

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

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

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.

prove by using the principle of similar triangles that: in a right angle triangle, the square on the hypotenuse is equal to the sum of squares on the two other sides. (Pythagoras theorem)

The hypotenuse of a right angle triangle is 6 cm more than twice the shortest side.If the third side is 2cm less than the hypotenuse ,find the sides of the triangle.

Prove that the areas of two similar triangles are in the ratio of the squares of their corresponding angle bisector.

The sides of a right angled triangle is in A.P with common difference 4.Find the sides.

The atitude of a right triangle is 7 cm less than its base.If the hypotenuse is 13 cm,find the other two sides.