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.

What does the theorem on the ratios of areas of two similar triangles state?

• The ratio of their areas is equal to the ratio of their altitudes.

• The ratio of their areas is equal to the ratio of their angles.

• The ratio of their areas is equal to the ratio of the squares of their corresponding sides.

• The ratio of their areas is equal to the ratio of their perimeters.

What is the first step in verifying the theorem using a triangle?

• Construct a right-angled triangle.

• Construct an isosceles triangle.

• Construct an equilateral triangle.

• Construct a scalene triangle.

How are the sides of the triangle divided in the construction process?

• Into 6 equal parts.

• Into 5 equal parts.

• Into 4 equal parts.

• Into 3 equal parts.

What is the purpose of drawing lines parallel to the sides of the triangle?

• To measure the angles of the triangle.

• To divide the triangle into smaller congruent triangles.

• To find the perimeter of the triangle.

• To create a larger triangle.

How many smaller triangles is triangle XYZ divided into?

• 16 smaller triangles.

• 30 smaller triangles.

• 25 smaller triangles.

• 20 smaller triangles.

What is the ratio of the areas of the smaller triangle to the larger triangle?

• 9:25

• 16:25

• 9:16

• 4:9

What conclusion is drawn from the verification of the theorem?

• The ratio of the areas of two similar triangles is equal to the ratio of their perimeters.

• The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

• The ratio of the areas of two similar triangles is equal to the ratio of their altitudes.

• The ratio of the areas of two similar triangles is equal to the ratio of their angles.