Geometry Unit 5: Similarity

Unit Driving Question

How do we know when two geometric figures are similar?

Essential Questions

1. How do we know when two geometric figures are similar?

2. What relationships can be found between the angles and the sides of similar triangles/polygons?

3. How do we use similarity to prove relationships among figures or parts of figures?

Launch Task

Big Ideas for Development Lessons

Closure & Assessment

1 Lesson

4 Weeks (approximately 1 week per big idea)

1 Week

Triangles Task

Click on the links below to see each Big Idea's Lesson Overview (includes links to teacher notes and student activities)

1. Similar polygons are defined by their congruent angles and proportional sides

2. Congruent corresponding angles and proportional corresponding sides are used to prove triangles are similar.

1. Formative Assessment 1 (after Big Idea 2)

2. Re-engagement Activity (Not Provided)

3. Unit Assessment (Not Provided)

Big Idea 1: Similar polygons are defined by their congruent angles and proportional sides.

OAS-M: G.2D.1.7

Lessons and Additional Activities

Big Idea 1 Lessons 1-3 Overview (includes links to teacher notes and student activities)

Evidence of Understanding

• Write similarity statements based off of corresponding sides and congruent angles.

• Use markings and geometric notation to identify congruent angles and proportional sides.

• Recognize the order of the vertices represent which sets of angles or sides are corresponding.

• When knowing two figures are similar use corresponding sides to find their scale factor.

• Use similarity statements to set up a ratio of side to side and simplify to determine the relationship between two similar figures.

• When knowing two figures are similar, use proportional relationships found within those figures to solve for missing sides.

• Use similarity statements to set up two congruent ratios as a proportion to solve for any missing side.

Big Idea 2: Congruent corresponding angles and proportional corresponding sides are used to prove triangles are similar.

OAS-M: G.2D.1.7

Lessons and Additional Activities

Big Idea 2 Lessons 1-3 Overview (includes links to teacher notes and student activities)

Evidence of Understanding

• Use markings and notations to identify congruent corresponding angles and proportional corresponding sides of triangles

• Map figures onto one another in the plane and identify corresponding angles and sides

• Use information about triangle similarity and congruence to determine which information is required to prove figures are similar

• Apply properties of parallel lines to prove figures are similar

• Apply angle relationships to prove figures are similar

• Example: Vertical Angles, Alternate interior, etc.

• Find missing values by applying the relationships of sides (scale factor) and angles

• Use similarity theorems such as Side-Angle-Side similarity, Side-Side-Side similarity, Angle-Angle similarity to write formal and informal proofs to prove that two triangles are similar