Lesson #2 - Augsburg College

Lesson #1: Introduction to Triangles
Approximate lesson length: 2-3 days
Lesson Objectives:
• Explore the triangle inequality
• Understand why the area of a triangle = 1/2 × base × height
Materials:
• Paper and pencil
• Graph paper
• Ruler
• Scissors
Part 1: What is a Triangle?
Geometry: A Shapely Approach to Math
Let’s start with the most basic question regarding triangles: What is a triangle? Ask your students this question
and let them brainstorm different definitions. Encourage them to be specific with their definitions. For example,
if a students says that a triangle has three sides, draw three lines that don’t connect and ask the student
why this is not a triangle. One possible definition of a triangle is that it is a three-sided figure with each line
crossing the other two lines at two different points.
Now ask your students to each draw a triangle, and then to look at the lengths of the sides of their triangles.
What do they notice if they compare the length of one side compared to the sum of the lengths of the other two
sides? Ask your students to draw a triangle in which the sum of the lengths of two of the sides is less than the
length of the third side. (This is impossible.) Your students will find that the third side is simply too long to ever
connect with the other two sides. Encourage them to use a ruler so they know they are measuring exactly. For
example, below the student would begin with drawing a side of length 3 connected to a side of length 4. Then,
their task would be to draw a third side of length greater than 7. But as we can see in the illustration, the side
drawn of length 7 is too long to make a triangle.
Next ask your students if it’s possible to draw a triangle such that the sum of the lengths of two sides equals
the length of the third side. Ask your students to draw a picture of what a triangle like this would look like. Following
is an example of a picture your students might draw. There is only one line in this “triangle.” Note that
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