Lesson objective: Fluently determine similarity in triangles by identifying equivalent relationships of the sides or identifying two pair of congruent corresponding angles.

This lesson helps to build fluency with the attributes of similar shapes. Triangle side lengths and angles are used here because similarity of triangles can be determined from two pairs of corresponding angles being congruent or a consistent scale factor. This work develops students' understanding that a triangle resulting from a series of transformation (dilations, rotations, reflections, or translations) is similar to the original triangle because two pairs of corresponding angles are congruent.

Students engage in Mathematical Practice 6 (attend to precision) as they use precise measurements when discussing similar triangles. Students should not assume shapes are similar without either identifying angles are congruent or given the shapes are similar.

**Key vocabulary:**

- acute triangles
- corresponding angles
- equilateral triangles
- isosceles triangles
- obtuse triangles
- right triangles
- scalene triangles
- similarity
- transformation
- vertical angles

**Special materials needed:**

- grid paper
- protractors
- rulers