1. 7.1 Apply the Pythagorean Theorem
Before: You learned about relationships within triangles
Now: You will find side lengths in right triangles.
Why?: So you can find the shortest distance between objects.

2. Pythagorean Theorem Basics
In a right triangle, the sum of the squares of the measures of the legs equals the square of the hypotenuse.
Legs: the two shorter sides, either can be a and b
Hypotenuse: the longest side, opposite the right angle
Only works for Right Triangles

3. Equations for Finding Side Lengths

4. Identify the legs and hypotenuse

5. Find the Length of the Unknown Side
Is the unknown side a leg or the hypotenuse?
Which equation should be used?

6. Identify the unknown side as a leg or hypotenuse. 2
Identify the unknown side as a leg or hypotenuse. 2. Find the length of the unknown side. Write your answer as a simplified radical

7. Similarity Proof of the Theorem

8. Find the area of an isosceles triangle
Step 1:Draw a sketch of the isosceles triangle.
The altitude of a triangle is the height of the triangle
Step 2:Use the Pythagorean theorem to find the height
Step 3: Find the Area

9. Find the area of an isosceles triangle
Sketch the Isosceles Triangle
Find the Height
Use Pythagorean Theorem
Find the Area

10. Your Turn
Find the area of the triangle.

11. Pythagorean Triples
Pythagorean Triple: A set of three positive integers a, b, and c that satisfy the equation

12. Find the Unknown side of the right triangle
Hint: Check for Pythagorean triples

13. Pythagorean Rap

14. Assignment
Pg 436 # 1-25 odd, 31, 32