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Lesson 9-7 - Special Right Triangles

OK, so I don't say this often, but I really mean it today...this could be one of the most important lessons we have all year. You'll use the results of this lesson more than almost anything else you learn this year. Granted, most of this use will be on other math problems throughout your high school and college careers, but let's face it...if you learn it now, you'll do better later!

We started today's lesson by looking at the following examples of problems involving isosceles right triangles:

Isosceles triangle Example 1


Isosceles triangle Example 2


Isosceles triangle Example 3


At this point, I asked if anyone noticed a pattern and a few of you did. The result is shown below:

45-45-90 General Case

This, in turn, leads to the following theorem:

The Isosceles Triangle Theorem

Next, we looked at 30-60-90 (a.k.a. 30-60-Right) triangles. To do this, we first looked at an equilateral triangle, from which we were able to derive some interesting facts about a 30-60-90 triangle:

Example using 30-60-90 Triangle

You should be able to see how we came up with the last conclusion - if you can't follow it through step by step until you can!

We then looked at the following example:

2nd Example using 30-60-90 Triangle

Why did we know the hypotenuse was 8? If you don't know, then look at the previous diagram and figure it out!!

At this point, we generalized in the following theorem:

30-60-90 Triangle Theorem

To conclude, we drew the following two special triangles. Please, please, please....memorize these!! If you do, you'll thank me many times over the next couple of years...

The two Special Right Triangles

Other Links
Class Notes
Lesson 9-1
Lesson 9-2
Lesson 9-3
Lesson 9-4
Quiz Topics
Lesson 9-5
Lesson 9-6
Lesson 9-7
Lesson 9-8
Lesson 9-9
Lesson 9-10
Test Topics
Trig Table
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