Geometry: Lesson 6.3 – Special Right Triangles

Geometry: Lesson 6.3 – Special Right Triangles Geometry Oklahoma Academic Standards: G.RT.1.2 Verify and apply properties of right triangles, including properties of 45-45-90 and 3060-90 triangles, to solve problems using algebraic and logical reasoning.

Lesson Objectives:

1. To prove and use the 45-45-90 right triangle to solve problems. 2. To prove and use the 30-60-90 right triangle to solve problems.

Introduction: In the last lesson, we proved the Pythagorean theorem and used it to prove other theorems and solve problems. In this lesson, we will prove, using the Pythagorean theorem, 2 very unique and special right triangles. These 2 special right triangles are

fundamental in upper level mathematics and construction in the real-world. The first of these two special triangles is the 45-45-90 right triangle. Given: ___________________________

Prove: ___________________________ Proof:

Geometry: Lesson 6.3

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Vocabulary: Theorem– The 45-45-90 Right Triangle

Example 1: Use the 45-45-90 Right triangle to find the missing side lengths below. a.)

b.)

_________________________________

_________________________________

c.)

_________________________________ What’s different about this one?

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Sometimes the square root of 2 is not on the hypotenuse like it is supposed to be. Therefore, we need an alternative form of the 45-45-90 triangle to handle this situation.

Vocabulary: Theorem– The 45-45-90 Right Triangle (Alternative Form)

Assignment 6.3a You have the choice of the following:

1. Complete the handout, “Geometry: Handout 6.3a” with a partner and turn it in.

2. Complete the handout, “Geometry: Handout 6.3a” by yourself and turn it in.

Geometry: Lesson 6.3

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We can use the Pythagorean Theorem to prove the second special right triangle known as the 30-60-90 right triangle.

Given: ___________________________

Prove: ___________________________ Proof:

Vocabulary: Theorem– The 30-60-90 Right Triangle

Like the 45-45-90 right triangle, there is an alternative form when the square root has been moved.

Geometry: Lesson 6.3

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Vocabulary: Theorem– The 30-60-90 Right Triangle (Alternative Form)

Example 3: Use the 30-60-90 right triangle to find the missing side lengths. a.)

b.)

______________________________

______________________________

c.)

d.)

______________________________

______________________________ Assignment 6.3b

You have the choice of the following:

1. Research a profession that uses special right triangles in common practice. What are ways they incorporate the math in their projects/business?

2. Complete the handout, “Geometry: Handout 6.3c” and turn it in. Geometry: Lesson 6.3

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