If the measures of the medians of a triangle are equal then prove that the triangle is equilateral.

If the areas of a similar triangle are equal,prove that they are congruent.

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.

Assuming the validity of the statement that the internal bisectors of the angles of a triangle are concurrent, prove that the altitudes of a triangle are concurrent.

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.

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.

The sides of a triangle measure 13 cm,12 cm,and 5 cm.prove that the triangle is right angled.

The vertices of a triangle are (a, 0), (-a, 0) and (0, sqrt(3a)) . Show that the triangle is equilateral.

Prove that the Pedal triangle of an equilateral triangle is also an equilateral triangle.

The medians of a triangle are 6 cm, 7.5 cm and 9 cm. Construct the triangle.

The sum of the degree measures of the three angles of a triangle is 180. The measure of the 2nd angle exceeds that of the 1st by 8 and the measure of the 3rd angle is twice of that of the 2nd. Find the measure of each angle.