1. Lesson 35: Special Right Triangles and the Pythagorean Theorem
Texas Algebra I
Lesson 35:
Special Right Triangles and the Pythagorean Theorem

2. Lesson objectives: The student will be able to:
Use the Pythagorean theorem to find the missing length of a side of a right triangle.
Identify and use the relationships of and isosceles right triangles
Identify Pythagorean “triples”

3. Pythagorean Theorem
The sum of the square of the legs, a and b, of a right triangle is equal to the square of hypotenuse, c. Algebraically expressed: a² + b² = c² Huh? Okay, let’s look at a picture!

4. Classic Pythagorean Proof

5. Special Right Triangles
Pythagorean Triples
All 3 side lengths are whole numbers
Any ratio of triples will work!
Examples:
3-4-5

6. Special Right Triangles
Isosceles right
Legs congruent
Hypotenuse length is equal to the length of the leg ×√2

7. Special Right Triangles
Half of an equilateral triangle
Shortest leg half the length of the side of the equilateral
Longer leg is equal to the length of the short leg ×√3

8. Practice Problems
The figure is a parallelogram. Find the missing length:

9. Practice Problems
Find the missing length:

10. Lesson objectives: The student will be able to:
Use the Pythagorean theorem to find the missing length of a side of a right triangle.
Identify and use the relationships of and isosceles right triangles
Identify Pythagorean “triples”