Lesson 17: Practice Problems

Problem 1

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

A triangle where one angle measures $20^{\circ}$ and another angle measures $45^{\circ}$
A triangle where one angle measures $120^{\circ}$ and another angle measures $50^{\circ}$
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.

Sketch this triangle and label your sketch with the given measures.
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.

Two diagrams-A triangle with one side 5 units long and an adjacent angle that measures 25 degrees with differing adjacent side lengths.

Problem 5

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.