# Lesson 17

Drawing Triangles

### Lesson Narrative

In the previous lesson, students were given collections of triangles and noticed that they shared angle and side measures, and that sometimes there was more than one type of triangle with the same measures. In this lesson, they build on that experience by drawing their own triangles with specified measures: a given angle, two given angles, and two given angles with a given side length (MP7). The purpose of this lesson is to give students experience using various tools to draw triangles with given conditions, and to help them see that sometimes the given conditions allow only one possible triangle, sometimes more than one, and sometimes none. Students are not expected to know rules about which conditions determine each possibility.

### Learning Goals

Teacher Facing

• Draw triangles with two given angle measures and one side length, and describe (orally) how many different triangles could be drawn with the given conditions.
• Draw triangles with two given side lengths and one angle measure or three given angle measures, and describe (orally) how many different triangles could be drawn with the given conditions.
• Use drawings to justify (in writing) whether two given angle measures and one side length determine one unique triangle.

### Student Facing

Let’s see how many different triangles we can draw with certain measurements.

### Required Preparation

To help students see how they can use a compass to draw different triangles with two of the same side lengths, you might choose to copy the How Many Can You Draw? blackline master for every student. This is optional.

### Student Facing

• Given two angle measures and one side length, I can draw different triangles with these measurements or show that these measurements determine one unique triangle or no triangle.
• Given two side lengths and one angle measure, I can draw different triangles with these measurements or show that these measurements determine one unique triangle or no triangle.