# Lesson 12

Practice With Proportional Relationships

### Lesson Narrative

This optional lesson gives students an additional opportunity to practice finding unknown values in proportional relationships using contextual examples. The problems preview using the Pythagorean Theorem, which is a key idea in a subsequent lesson. They also preview finding all unknown values in right triangles, which is a key idea in a subsequent unit. Students have a chance to reason abstractly and quantitatively as they think about whether their answers make sense in context (MP2).

### Learning Goals

Teacher Facing

• Calculate unknown values in proportional relationships.
• Determine scale factors to describe similar figures (using words and other representations).

### Student Facing

• Let’s find unknown values in proportional relationships.

### Student Facing

• I can find scale factors and use them to solve problems.

### Glossary Entries

• similar

One figure is similar to another if there is a sequence of rigid motions and dilations that takes the first figure onto the second.

Triangle $$A'B'C'$$ is similar to triangle $$ABC$$ because a rotation with center $$B$$ followed by a dilation with center $$P$$ takes $$ABC$$ to $$A'B'C'$$.