Ratios of Areas of Similar Triangles

The video tutorial explains the theorem on the ratios of areas of two similar triangles, stating that the ratio of their areas is equal to the ratio of the squares of their corresponding sides. The tutorial demonstrates this by constructing an equilateral triangle XYZ, dividing it into smaller triangles, and painting them. A smaller triangle with sides 3/5 of XYZ is also constructed. The theorem is verified by comparing the areas of the smaller triangles, confirming that the ratio of the areas matches the ratio of the squares of the sides.

Explain how the areas of the smaller triangles relate to the areas of the larger triangles.

What conclusion can be drawn from the ratio of the areas of triangle element and triangle XYZ?

How does the theorem verify that the ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides?