8.01 Similar Right Triangles

• Introduction
• Learn
• Try It
• Task

Introduction

In this lesson, we will explore similar right triangles. Go through the GeoGebra activity Similar Right Triangles (II) activity and think about these questions as you work through it.

1. What is the sum of the measures of the red and green angles? How do you know this to be true?
2. The segment that was drawn as you dragged the slider is called an altitude. This altitude was drawn to the hypotenuse. How many right triangles did this altitude split the original right triangle into?
3. What does the special movement of the red and green angles imply about these 2 smaller right triangle? What previously learned postulate or theorem justifies your answer?
4. Does your response for (3) also hold true for the relationship between the ORIGINAL BIG RIGHT TRIANGLE and either one of the smaller right triangles? If so, how/why do you know this?

 

Lesson Objectives

Following successful completion of this lesson, students will be able to... solve problems and prove relationships in right triangles with an altitude drawn from the vertex of the right angle to the hypotenuse using congruence and similarity criteria for triangles Enduring Understandings The special properties of right triangles can be used to solve real world problems. The above objectives correspond with the Alabama Course of Study: Geometry standard: 18