If the areas of two similar triangles are equal, prove that they are congruent.

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

Define : Similar triangles

State whether each of the following statements is true or false : The areas of two similar triangels are propotional to their correspoonding sides.

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.

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.

Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : The ratio of the perimeters of two similar triangles is 4 : 25, then the ratio of their areas is……..

State whether each of the following statements is true or false : If the areas of two sectors of two different circles are equal, the lengths of their corresponding arcs are equal.

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

Any two similar figures are congruent.

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram.