Lesson #3: Triangles

By Rebecca Adcock

Right Triangles

A right triangle is any triangle that has one angle equal to 90 degrees. In the triangle below, the right angle is BCA. The longest side of a right triangle is called the hypotenuse and it is the side opposite the right angle. AB (also called c) is the hypotenuse. BC (also called a) and AC(also called b) are legs.

Pythagorean Theorem

You’ve already encountered the Pythagorean Theorem somewhere in your study of mathematics. Recall that the Pythagorean Theorem states

“In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.”

If you don’t remember those words exactly, you probably remember this:

Special Right Triangles. 30-60-90 Triangle

We will create a 30-60-90 triangle by bisecting one angle of an equilateral triangle. The two triangles created are congruent, but we will concentrate on just one of them. In triangle ABC (at left), each side is equal. AB=BC=AC. BD bisects angle ABC so BD also bisects side AC. So AD=DC and AD =1/2(AB).

By Pythagorean Theorem,

Let the length of side AB equal 1. So BC=1, AC=1 and AD=1/2.

Special Right Triangles. 45-45-90 Triangle

Check your understanding. See Lesson #3 in Lesson Assessments.

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