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

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 medians of an equilateral triangle are equal.

Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y =4 and the opposite vertex of the hypotenuse is (2,2) .

Prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side. (Using converse of basic proportionality theorem)

Prove using vectors: The median to the base of an isosceles triangle is perpendicular to the base.

If the lengths of the sides of a triangle are decided by the three thrown of a single fair die,then the probability that the triangle is of maximum area given that it is an isosceles triangle, is

Prove that two triangles on the same base and between the same parallels are equal in area.

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1 (1)/(2) thimes the corresponding sides of the isosceles triangle.

Form the bicoditional statement phArrq . Where p: A triangle is an equilateral triangle. q: All three sides of a triangle are equal.

Write down the contrapositive of the following statements.: If all three sides of a triangle are equal, then the triangle is equilateral.