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.

If two medians of a triangle are equal, prove that the triangle is isosceles.

Find counter-examples to disprove the following statement: If the corresponding angles in two triangles are equal, then the triangles are congruent.

In a squared sheet, draw two triangles of equal areas such that the triangles are congruent. What do you say about its perimeters?

In a squared sheet, draw two triangles of equal areas such that the triangles are not congruent. What do you say about its perimeters?

Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, using RHS congruence rule. In case of congruent triangles, write the result in symbolic form:

Given below are measurements of some parts of two triangles . Examine whether the two triangles are congruent or not, by ASA congruence rule. In case of congruence, write it in symbolic form.

Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by using SAS congruence rule. If the triangles are congruent, write them in symbolic form. (It will be always helpful to draw a rough figure, mark the measuremants and then probe the question).

Two angles are congruent if they are:

If two right triangles, one side and an acute angle of one triangle are equal to one side and the corresponding angle of other triangle. Prove that the two triangles are congruent.