Unit Overview:
This unit builds on the students knowledge of transformations and introduces a new transformation, dilation, that does not preserve congruence. They will use the properties of similarity transformations to prove theorems about triangles and develop AA criterion for two triangles to be similar. Students will solve problems using congruence and similarity criteria. The properties and theorems of similarity covered in this unit will be applied to the definitions of trigonometric ratios in the following unit.
Enduring Understanding:
Essential Question:
This unit builds on the students knowledge of transformations and introduces a new transformation, dilation, that does not preserve congruence. They will use the properties of similarity transformations to prove theorems about triangles and develop AA criterion for two triangles to be similar. Students will solve problems using congruence and similarity criteria. The properties and theorems of similarity covered in this unit will be applied to the definitions of trigonometric ratios in the following unit.
Enduring Understanding:
- Scaled drawings are created through proportions and similarity.
- Understand the definition of similarity in terms of dilations.
Essential Question:
- How do dilations differ from isometric transformations?
- How do you determine if two figures are similar?
- How do the properties of dilations justify the AA similarity theorem?
- How can congruence and similarity with triangles be used to prove relationships in geometric figures?
