# Lesson 3

Half an Equilateral Triangle

### Lesson Narrative

This lesson is optional. It builds on the thinking that students did in the previous optional lesson. It is recommended to only do this lesson along with the previous optional lesson.

Many standardized assessments provide the special triangle relationships as a reference and ask students to reason about similar triangles. This lesson gives students an opportunity to apply their reasoning about similar figures and their skill with the Pythagorean Theorem to make sense of the relationship and understand how they might use a reference diagram to solve problems.

Students have an opportunity to reason abstractly and quantitatively (MP2) as they both measure lengths in, and solve analytically, 30-60-90 triangles.

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.

### Learning Goals

Teacher Facing

- Calculate side lengths in 30-60-90 triangles.
- Generalize the properties of 30-60-90 triangles including side lengths and ratios (using words and other representations).

### Student Facing

- Let’s investigate the properties of altitudes of equilateral triangles.

### Required Materials

### Learning Targets

### Student Facing

- I can determine the side lengths of triangles with 30, 60, and 90 degree angles.