## Geometry

### Similarity and Proportion

Similarity is more than "same shape, different size." In this unit, students develop a more formal definition of similarity in lessons emphasizing that similar figures have congruent corresponding angles and proportional corresponding sides. They identify the corresponding parts of similar triangles, discover minimal requirements to guarantee similarity, investigate special cases such as nested triangles, and explore the relationships for area and perimeter of similar figures.

### Geometry: Similarity and Proportion Activities

Title Type

#### Applications of Similar Figures

Students will identify corresponding parts of figures and use the definition of similar figures to solve real-world applications involving rectangles and triangles.

• 2384

#### Similar Figures

Observe what happens to ratios of pairs of side of rectangles and triangles.

• 7095

#### Corresponding Parts of Similar Triangles

Change the scale factor (r) between similar triangles; identify the corresponding parts and establish relationships between them.

• 6799

#### Angles and Similarity

Experiment with the measures of the angles of similar triangles to determine conditions necessary for two triangles to be similar.

• 6953

#### Nested Similar Triangles

Discover the conditions that make triangles similar by moving the sides opposite the common angle in nested triangles.

• 6449

#### Triangle Midsegments

Investigate the relationships between a triangle and the similar triangle formed by one of the triangle's midsegments.

• 6458

#### Scale Factor Area Perimeter

Explore the relationship of perimeter and area in similar triangles when the scale factor is changed.

• 6537

#### Ratios of Similar Figures

Students explore the ratio of perimeter, area, surface area, and volume of similar figures in two and three dimensional figures.

• 4835