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 \(50^\circ\)
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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 images, each a segment with side 5 and a dotted line rising at a 25 degree angle from the segment.](https://cms-im.s3.amazonaws.com/JCtfx5hUae7VFyxFFbC2YGVh?response-content-disposition=inline%3B%20filename%3D%227-7.7.newPP.twotriangles005.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.newPP.twotriangles005.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T181450Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f27ebce9a4e16da55d73285cdd44d87ad3fbb3c14727b76f3a975f26842c7e19)
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.