Introduction

Students often want to know if they will ever use the math concepts they are learning in school. It’s a good question. The angle relationships in a triangle are a good example of how these concepts are useful in real-world applications. Did you know that the theorem for the interior angles of a triangle is how your phone’s GPS locates you?

smart phone with GPS

Today we will focus on the angle relationships in any triangle.

Go to GeoGebra: ACCESS - Sum of Angles in a Triangle. Notice what the sum of the interior angles equal.

Then, go to GeoGebra: ACCESS - Exterior Angles. Also do you notice anything about the sum of two of the interior angles?

Download and complete 6.01 Explore. When you have finished, submit it to the 6.01 Explore Dropbox.

 

Lesson Objectives

Following successful completion of this lesson, students will be able to...

  • Classify triangles by their sides and angles
  • What are the differences between acute, right, and obtuse triangles?
  • Investigate and use angle addition theorem to solve problems with triangles
  • Identify and use the triangle sum and exterior angle theorems of a triangle
  • Prove theorems about triangles

Essential Questions

  • What are the differences between isosceles, scalene, and equilateral triangles?
  • What are the differences between acute, right, and obtuse triangles?
  • How do you find the perimeter and area of a triangle in the coordinate plane?
  • What information is needed to show that two triangles are congruent?
  • What information is needed to show that two figures are congruent?

Enduring Understandings

  • The symmetry of polygons can be described in rotations and reflections.
  • The sum of the interior angles of any triangle is a constant.
  • The perimeter and area of a polygon can be calculated using its x and y coordinates.
  • Congruence can be used to prove theorems about triangles.

The above objectives correspond with the Alabama Course of Study: Geometry standard: 29, 29a, 31b.