1. Pythagorean Theorem Advanced Geometry Trigonometry Lesson 1

2. Examples: Simplify

3. Multiplying Radicals * Multiply first. *Then simplify. Example: Simplify

4. Dividing Radicals Examples: 1) Both #’s are perfect squares. Take the square root. Divide then simplify. 3 CASES 2) The #’s are divisible. 3) Rationalize the denominator.

5. If there is a radical in the denominator, you must rationalize the denominator.

6. Rules for Simplifying Radical Expressions 3. There can be no radicals in the denominator of a fraction. 1. All radicals must be fully simplified. 2. There can be no fractions under a radical.

7. Example: Find the geometric mean between each pair of numbers. Geometric Mean 20 and 35

8. The measure of an altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the segments of the hypotenuse. THEOREM

9. Example: In ABC, BD = 6 and AD = 27. Find CD.

10. In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. Pythagorean Theorem

11. The Pythagorean Theorem can be used to verify whether a triangle is a right triangle or not. A Pythagorean triple is three whole numbers that satisfy the Pythagorean Theorem. 3, 4, 5For instance;

12. Examples: Determine whether each set of measures can be the sides of a right triangle. Then state whether they form a Pythagorean triple. 8, 12, 16 ? ? Not a Right Triangle