Theorem If the Altitude Is Drawn to the Hypotenuse of a Right Triangle, Then the Two New

CHAPTER NINE

·  Theorem – if the altitude is drawn to the hypotenuse of a right triangle, then the two new smaller triangles formed are similar to one another and the original triangle

·  Theorem – in a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The geometric mean of those two segments is the measure of the altitude.

·  Theorem – – in a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

·  Pythagorean Theorem – in a right triangle, a2 + b2 = c2 where a and b are the legs of a right triangle and c is the hypotenuse

·  Converse of the Pythagorean Theorem – if c2 = a2 + b2 , then the triangle is a right triangle

·  Theorem - c2 a2 + b2 then the triangle is an acute

·  Theorem - c2 > a2 + b2 then the triangle is an obtuse

·  45-45-90 Triangle Theorem – each of the legs of a right triangle measuring 45-45-90 have the same length and the hypotenuse measures the length of a leg times

·  30-60-90 Triangle Theorem – the leg opposite the 30° angle is the starting measure, the leg opposite the 60° angle measures the leg opposite the 30° angle times and the hypotenuse is twice the measure of the leg opposite the 30° angle.

·  Sine (SIN) =

·  Cosine (COS) =

·  Tangent (TAN) =

SOH CAH TOA

·  Solve a Right Triangle means to determine the measures of all three angles and all three sides of a given triangle

·  Vector – a quantity that has both magnitude and direction

·  Initial Point – starting point

·  Terminal Point – ending point

·  Magnitude of a Vector – is the distance from the initial point to the terminal point (Use the distance formula.)

·  Direction of a Vector is determined by the angle a vector makes with a horizontal line. It is states as North, South, East, West, Northeast, Northwest, Southeast or Southwest

·  Two vectors are equal if they have the same magnitude and direction

·  Two vectors are parallel if they have the same or opposite directions (think same slope)

·  Sum of Two Vectors – the sum of two vectors means adding the x-coordinates together to form a new x-coordinate and adding the y-coordinates together to form a new y-coordinate