Sullivan Algebra and Trigonometry: Section R.3 Geometry Review Objectives of this Section Use the Pythagorean Theorem and Its Converse Know Geometry Formulas

A right triangle is on that contains a right angle, that is, an angle of 90°. The side opposite the right angle is the hypotenuse. The Pythagorean Theorem 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.

Example: The Pythagorean Theorem Show that a triangle whose sides are of lengths 6, 8, and 10 is a right triangle. We square the length of the sides: Notice that the sum of the first two squares (36 and 64) equals the third square (100). Hence the triangle is a right triangle, since it satisfies the Pythagorean Theorem.

Converse of the Pythagorean Theorem In a triangle, if the square of the length of one side equals the sums of the squares of the lengths of the other two sides, then the triangle is a right triangle. The 90 degree angle is opposite the longest side.

For a rectangle of length L and width W: For a triangle with base b and altitude (height) h: Geometry Formulas For a circle of radius r (diameter d = 2r)

Geometry Formulas For a rectangular box of length L, width W, and height H: For a sphere of radius r: For a right circular cylinder of height h and radius r: