If two angles and the included side of one triangled are euqal to two angles and the included side of the other triangle, prove that those two triangles are congruent.

If the areas of two similar triangles are equal, prove that they are congruent.

If the angles of a triangle are 30^(@) and 45^(@), and the included sise is (sqrt3+ 1) cm, then prove that the area of the triangle is 1/2 (sqrt3+1).

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

If the lengths of sides of right angled triangle are in A.P then the sines of the acute angles are

For any triangle, prove that the sum of the sides of the triangle is greater than the sum of the medians of the triangle.

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

Write down the converse of following statements: If the sum of squares of two sides foa triangle is equal to the square of third side of a triangle, then the triangle is right angled.

Prove that the angles opposite to equal sides of an isosceles triangle are equal.

Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio

If two angles of a triangle are tan^(-1)(2) and tan^(-1)(3), then find the third angle.