Advanced Geometry Trigonometry Lesson 1 Pythagorean Theorem Examples

Advanced Geometry Trigonometry Lesson 1 Pythagorean Theorem

Examples: Simplify

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

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

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

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

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

THEOREM 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.

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

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

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. For instance; 3, 4, 5

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