Understanding Dilations and Similar Figures

The video tutorial explains the concept of similar figures, focusing on how shapes that are dilations of each other maintain the same angles but have different side lengths proportional to a scale factor. It covers the calculation of scale factors by dividing new side lengths by old ones and provides examples of similar triangles, demonstrating how to determine if triangles are similar by checking proportionality of their sides. The tutorial also discusses applying dilation to triangles and calculating missing side lengths using the scale factor.

What is a key characteristic of similar figures?

• They have the same size.

• They have non-proportional sides.

• They have equal angles.

• They have different shapes.

What happens to the angles of a figure after dilation?

• They become zero.

• They halve.

• They double.

• They remain the same.

How do you calculate the scale factor between two similar figures?

• Multiply the old side by the new side.

• Divide the new side by the old side.

• Add the old side to the new side.

• Subtract the old side from the new side.

If a triangle has sides 2, 3, and 5, what must be true for another triangle to be similar?

• The sides must be 2, 3, and 6.

• The sides must be 4, 6, and 10.

• The sides must be 1, 1.5, and 2.5.

• The sides must be 3, 4, and 5.

What is the scale factor if a side of a triangle changes from 3 to 6?

• 0.5

• 1

• 2

• 3

In a similar triangle, if one side is 8 and the corresponding side in the original is 4, what is the scale factor?

• 2

• 4

• 1

• 0.5

How do you determine if two triangles are similar?

• By checking if they have the same area.

• By checking if they have the same perimeter.

• By checking if their angles are equal.

• By checking if their sides are proportional.

If a triangle with sides 6, 9, and 15 is similar to another triangle, what is the common scale factor?

• 2

• 4

• 1

• 3

If a side of a triangle is 5 and its corresponding side in a similar triangle is 10, what is the scale factor?

• 2

• 1

• 5

• 0.5

In a dilation, if the original side length is 3 and the new side length is 9, what is the scale factor?

• 1

• 2

• 3

• 4