Understanding Dilations and Similar Triangles

This lesson covers the concept of dilations in geometry, explaining how they create similar triangles by maintaining proportional sides and congruent angles. It reviews the properties of dilations, including the role of the center of dilation and the scale factor. The lesson also discusses the angles formed by parallel lines cut by a transversal, such as alternate interior, corresponding, and alternate exterior angles. It concludes by verifying that dilations are similarity transformations, ensuring that all corresponding angles and sides are congruent and proportional, respectively.

What is the result of a dilation transformation?

• An image with the same shape and size

• An image with a different shape but same size

• An image with a different shape and size

• An image with the same shape but different size

What is the role of the center of dilation in a transformation?

• It is the midpoint of the image

• It is the endpoint of the pre-image

• It is the point from which the dilation originates

• It determines the direction of the transformation

Which of the following is true about alternate interior angles?

• They are not congruent

• They are congruent and located between parallel lines

• They are located outside the parallel lines

• They are on the same side of the transversal

What is the relationship between corresponding angles in parallel lines cut by a transversal?

• They are never congruent

• They are always supplementary

• They are always congruent

• They are always complementary

What must be true for two figures to be considered similar?

• All corresponding angles are congruent and sides are proportional

• All corresponding sides are equal

• All corresponding angles are different

• All corresponding sides are proportional but angles are different

How can we verify that a dilation is a similarity transformation?

• By checking that all sides are proportional but angles are different

• By ensuring all corresponding sides are equal

• By checking that all angles are different

• By confirming all corresponding sides are proportional and angles are congruent

In the example of triangles PQR and P'Q'R', what is used to verify similarity?

• The sum of angles being 180 degrees

• The sum of sides being proportional

• The sum of angles being 90 degrees

• The sum of sides being equal