prove that two isosceles triangles are similar if their vertical angles are equal. (it is supposed that the angle on the base of a triangle are equal).

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

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

Fill in the gap : Two triangles are similar if their _______ sides are proportional.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding altitudes of the triangles.

All____ triangles are similar. (isosceles, equilateral)

If one angle of a triangle is equal to one angle of another triangle and the bisectors of these equal angles divide the opposite side in the same ratio then show that the triangle are similar.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the bisectors of the corresponding angles of the triangles. [The end-points of the angular bisectors are on the opposite sides of the angles.]

Prove that in two equiangular triangles the ratio of the corresponding sides and the ratio of the bisectors of the corresponding angles are equal. [The end-points of the bisectors are on the opposite sides of the angles.]

Prove that the area of an equilateral triangle with sides equal to the sides of a square is half the area of the equilateral triangle with sides equal to țhe length of the diagonals of the square.

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.