9.1: Which One Doesn’t Belong: Triangles
Which one doesn’t belong?
9.2: Does Your Triangle Match Theirs?
Three students have each drawn a triangle. For each description:
Drag the vertices to create a triangle with the given measurements.
- Make note of the different side lengths and angle measures in your triangle.
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°.
9.3: How Many Can You Draw?
Draw as many different triangles as you can with each of these sets of measurements:
- Two angles measure \(60^\circ\), and one side measures 4 cm.
- Two angles measure \(90^\circ\), and one side measures 4 cm.
- One angle measures \(60^\circ\), one angle measures \(90^\circ\), and one side measures 4 cm.
Which sets of measurements determine one unique triangle? Explain or show your reasoning.
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.
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 \(100^\circ\):
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:
Any triangle drawn with these three conditions will be identical to the one above, with the same side lengths and same angle measures.