# Lesson 17

Drawing Triangles

### Problem 1

Use a protractor to try to draw each triangle. Which of these three triangles is impossible to draw?

1. A triangle where one angle measures $$20^\circ$$ and another angle measures $$45^\circ$$
2. A triangle where one angle measures $$120^\circ$$ and another angle measures $$50^\circ$$
3. A triangle where one angle measures $$90^\circ$$ and another angle measures $$100^\circ$$

### Problem 2

A triangle has an angle measuring $$90^\circ$$, an angle measuring $$20^\circ$$, and a side that is 6 units long. The 6-unit side is in between the $$90^\circ$$ and $$20^\circ$$ angles.

1. Sketch this triangle and label your sketch with the given measures.
2. How many unique triangles can you draw like this?

### Problem 3

A triangle has sides of length 7 cm, 4 cm, and 5 cm. How many unique triangles can be drawn that fit that description? Explain or show your reasoning.

### Problem 4

A triangle has one side that is 5 units long and an adjacent angle that measures $$25^\circ$$. The two other angles in the triangle measure $$90^\circ$$ and $$65^\circ$$. Complete the two diagrams to create two different triangles with these measurements.