Introduction

We have already explored several ways to prove that certain triangles are congruent (equal) by using the SSS and SAS theorems. These techniques are useful when working with triangles in real-world problems. Did you know there are even more ways to prove triangles are congruent?

traiangle shaped windows in a building

 

You've learned two ways to prove that triangles are congruent. Are there other ways?

Use GeoGebra: ACCESS - AAA and AAS? to complete the 6.06 Explore. Submit your completed work to the 6.06 Explore Dropbox.

 

Lesson Objectives

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

  • Prove two triangles are congruent using ASA and AAS
  • Identify and use rigid motions to prove t wo triangles are congruent

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: 25ba, 25b, and 31b.