Prove that three times the square of any side of an equilateral triangle is equal to four times the square of the altitude.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals

If the area of the square drawn on any side of a triangle is equal to the sum of the areas of the squares drawn on the other two sides of the triangle ,then the triangle will be right-angled triangle, the opposite angle of the greatest side of which will be "......................" .

Prove that the sum of the perpendiculars drawn from any interior point of an equilateral triangle to its sides then sum of three perpendiculars is equal to the altitude of the triangle.

Prove that if the difference of the areas of the squares drawn on any two sides of a triangle be equal to the area of square drawn ono its third side, then the triangle is a right-angled triangle.

The side of a square is a and each of the sides of an equilateral triangle is a. Then the ratio of their areas is

The diagonal of a square is 10sqrt(3)cm and the area of an equilateral triangle is equal to the area of the square. If a square is constructed on any side of the triangle, then find its area.

If the equilateral triangle DeltaAOB be into the square ABCD. Find angleCOD

A perpendicular AD is drawn on BC from the vertex A of the acute Delta ABC . Prove that AC^(2) = AB^(2) +BC^(2) -2BC.BD OR Prove that the square drawn on the opposite side of theacute angle of an acute triangle is equal to the areas of the sum of the squares drawn on its other two sides being subtracted by twice the area of the rectangle formed by one of its sides and the projection of the other side to this side.

Prove that if the three medians of a triangle be equal , then it is an equilateral triangle.