Lesson 17

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 $100^\circ$

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?

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.

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.

Is it possible to make a triangle that has angles measuring 90 degrees, 30 degrees, and 100 degrees? If so, draw an example. If not, explain your reasoning.