Properties and Transformations of Similar Figures

This lesson explores the basic properties of similarity, focusing on symmetric and transitive relationships. It demonstrates how to show that two figures are similar using sequences of transformations, including dilation and congruence. The lesson includes exploratory challenges to practice these concepts and concludes with a summary and instructions for further exercises.

What is required to demonstrate that two figures are similar?

• Only a dilation

• Only a congruence

• A sequence of transformations including dilation and congruence

• A reflection and a rotation

If figure S is similar to figure R, what does the symmetric property imply?

• Figure S is identical to figure R

• Figure R is not similar to figure S

• Figure R is similar to figure S

• Figure S is congruent to figure R

What is the transitive property of similarity?

• If S is similar to R and R is similar to T, then S is similar to T

• If S is similar to R, then R is not similar to S

• If S is similar to R, then S is congruent to T

• If S is similar to T, then T is not similar to R

Which transformation is NOT typically used to prove similarity?

• Dilation

• Translation

• Rotation

• Reflection

What should you rely on to check the similarity of triangles in the exit ticket?

• The color of the triangles

• The position of the triangles

• The drawn scale of the triangles

• The given side lengths