Right Triangles

Final Review

Click check to check your problems from Applications.

A radical expression is in its simplest form if :

No radicands have perfect sqaure factors other than 1
No radicands are fractions
No Radicals are in the denominator of a fraction

Definition Geometric Mean

The geometric mean between two positive numbers a,b is the number x such that

Similarity Theorem: The altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse creates two triangles, both of which are similar to the original triangle and each other.

Right Triangle Altitude Theorem :

Part a: The measure of the 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 two segments of the hypotenuse.

Part b: If the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.

From the theorems following facts follow:

ABC is similar to DAC

ABC is similar to DBA and

DAC is similar to DBA

And that the measures

1.

2.

3.

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

In the picture the above theorem states:

Pythagorean Thereom converse:

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Using the above triangle this means if then ABC is a right triangle.

Tests for Acute, Obtuse or Right Triangles:

In triangle ABC, if c is the longest side of the triangle, then

Relations of sides	Type of Triangle
	Acute
	Right
	Obtuse

Isosceles Right ()Triangle Theorem: In an isosceles right () triangle, the hypotenuse is times as long as a leg.

Triangle Theorem: In a triangle, the hypotenuse is twice as long as the shorter leg and the longer leg is times as long as the shorter leg.

Trigonometric Ratios Definition:

refer to the triangle to the right:

A mnemonic to help you remember the trigonometric ratios:

Some Old Horse:

Caught A Horse:

Taking Oats Away:

Steps for solving "word" problems:

1. Read the problem all the way through.

2. Read it again, drawing a picture of whatever you can.

3. Label the picture with all that is given.

4. Write down any givens not already in the picture.

5. Write down what you want to find out (the unknown).

6. Use any formulas in this lesson to write the unkown in terms of what is given.

7. Solve for the unknown using algebra.