Lesson 9Drawing Triangles (Part 1)
Learning Goal
Let’s see how many different triangles we can draw with certain measurements.
Learning Targets
Given two angle measures and one side length, I can draw different triangles with these measurements or show that these measurements determine one unique triangle or no triangle.
Warm Up: Which One Doesn’t Belong: Triangles
Problem 1
Which one doesn’t belong?
Activity 1: Does Your Triangle Match Theirs?
Problem 1
Three students have each drawn a triangle. For each description of a student’s triangle:
Drag the vertices to create a triangle with the given measurements.
Compare their measurements to the other 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
. Andre’s triangle has one angle measuring
and one angle measuring . Lin’s triangle has one angle measuring
, one angle measuring , and one side measuring 5 cm.
Print Version
Three students have each drawn a triangle. For each description:
Draw a triangle with the given measurements.
Measure and label the other side lengths and angle measures in your triangle.
Decide whether the triangle you drew must be an identical copy of the triangle that the student drew. Explain your reasoning.
Jada’s triangle has one angle measuring
. Andre’s triangle has one angle measuring
and one angle measuring . Lin’s triangle has one angle measuring
, one angle measuring , and one side measuring 5 cm.
Activity 2: How Many Can You Draw?
Problem 1
Draw as many different triangles as you can with each of these sets of measurements:
Two angles measure
, and one side measures 4 cm. Two angles measure
, and one side measures 4 cm. One angle measures
, one angle measures , and one side measures 4 cm.
Print Version
Draw as many different triangles as you can with each of these sets of measurements:
Two angles measure
, and one side measures 4 cm. Two angles measure
, and one side measures 4 cm. One angle measures
, one angle measures , and one side measures 4 cm.
Problem 2
Which of these sets of measurements determine one unique triangle? Explain or show your reasoning.
Are you ready for more?
Problem 1
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.
Lesson 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
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
Any triangle drawn with these three conditions will be identical to the one above, with the same side lengths and same angle measures.