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.