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

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

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 in a triangle r_1=r_2+r_3+r , prove that the triangle is right angled.

The ratio of the measures of the sides of a triangle is 3 : 4 : 5. If the semiperimeter of the triangle is 36 cm, the measure of the longest side of the triangle is …………..cm.

Using therem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in class IX).

In triangle ABC, AB = AC and the bisector of angle A lt intersects BC at D. Prove that, ( 1 ) triangle ADB = triangle ADC ( 2 ) angle ABC = angle ACB

In an equilateral triangle with side a, prove that, the area of the triangle (sqrt(3))/(4)a^(2) .

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.

In an equilateral triangle with side a, prove that, the altitude is of length (sqrt(3))/(2)a .