Geometry Chapter 8
Terms in this set (13)
If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
Converse of the Pythagorean Theorem
If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.
45-45-90 Triangle Theorem
In a 45-45-90 triangle, the legs are congruent and the length of the hypotenuse is is sqrt(2) times the length of the leg.
30-60-90 Triangle Theorem
In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the short leg. The length of the long leg is sqrt(3) times the length of the short leg.
Opposite leg/hypotenuse (o/h)
Adjacent leg/hypotenuse (a/h)
Sine/Cosine, Opposite leg/Adjacent leg (o/a)
Two numbers are multiplicative inverses of each other if they multiply to equal 1. (for all real number operations)
Law of Sines
For ANY triangle, 3 proportional relationships exist between the sine value of an angle and its opposite side.
Law of Cosines
For ANY triangle, this relationship exists (see picture).
Angle of elevation
The angle formed by "Looking upward" from a line parallel to the ground.
Angle of depression
The angle formed by a line parallel to the ground and someone "looking downward."
Area of a triangle (using sin)
(two adjacent sides)