Lesson 9

Drawing Triangles (Part 1)

Let’s see how many different triangles we can draw with certain measurements.

9.1: Which One Doesn’t Belong: Triangles

Which one doesn’t belong?

Four triangles, A, B, C, D.

 

9.2: Does Your Triangle Match Theirs?

Three students have each drawn a triangle. For each description:

  1. Drag the vertices to create a triangle with the given measurements.

  2. Make note of the different side lengths and angle measures in your triangle.  

  3. Decide whether the triangle you made must be an identical copy of the triangle that the student drew. Explain your reasoning.

Jada’s triangle has one angle measuring 75°.

Andre’s triangle has one angle measuring 75° and one angle measuring 45°.

Lin’s triangle has one angle measuring 75°, one angle measuring 45°, and one side measuring 5 cm.
 

 

9.3: How Many Can You Draw?

  1. Draw as many different triangles as you can with each of these sets of measurements:

    1. Two angles measure \(60^\circ\), and one side measures 4 cm.
    2. Two angles measure \(90^\circ\), and one side measures 4 cm.
    3. One angle measures \(60^\circ\), one angle measures \(90^\circ\), and one side measures 4 cm.

  2. Which sets of measurements determine one unique triangle? Explain or show your reasoning.

 


Nine toothpicks are arranged to make 3 equilateral triangles, their bases form a horizontal line.

In the diagram, 9 toothpicks are used to make three equilateral triangles. Figure out a way to move only 3 of the toothpicks so that the diagram has exactly 5 equilateral triangles.

Summary

Sometimes, we are given two different angle measures and a side length, and it is impossible to draw a triangle. For example, there is no triangle with side length 2 and angle measures \(120^\circ\) and \(100^\circ\):

Figure of a horizontal line segment with dashed line segments forming angles at each end.

Sometimes, we are given two different angle measures and a side length between them, and we can draw a unique triangle. For example, if we draw a triangle with a side length of 4 between angles \(90^\circ\) and \(60^\circ\), there is only one way they can meet up and complete to a triangle:

A segment 4 units long is drawn.  A dotted line is drawn perpendicular to one end of the segment, a dotted line is drawn at a 60 degree angle to the other end of the segment.  The dotted lines meet.

Any triangle drawn with these three conditions will be identical to the one above, with the same side lengths and same angle measures.