Lesson 17
Drawing Triangles
Let’s see how many different triangles we can draw with certain measurements.
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 6unit 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.
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.