Working With Triangles

The Pythagorean Theorem - states that if a and b are the length of the legs of a right triangle, and c is the length of the hypotenuse, then the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs,

c² = a^{2 +} b²

We can also say that if c² ≠  a^{2 +} b² , then the triangle is not a right triangle.

Distance Formula:

The distance between any two points (x₁, y₁ ) and (x₂, y₂ ) on a coordinate plane is:

Similar Triangles:

• The angels of one triangle and the corresponding angels of a second triangle have equal measures;

• The measures of the sides of the two triangles are proportional.

Trigonometric Ratios - the ratios of the measures of two sides of a right triangle.

sine of ∠A = measure of leg opposite ∠A

  measure of hypotenuse

cosine of ∠A = measure of leg adjacent to ∠A

        measure of hypotenuse

 

tangent of ∠A =   measure of leg opposite ∠A

measure of leg adjacent to ∠A

The e-Learning Research Foundation 2008