Download R.3 - Gordon State College

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.
2
2
a + b = c
2
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:
2
6 = 36
2
8 = 64
2
10 = 100
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.
Geometry Formulas
For a rectangle of length L and width W:
Area = lw Perimeter = 2l + 2w
For a triangle with base b and altitude (height) h:
1
Area = bh
2
For a circle of radius r (diameter d = 2r)
Area = p r 2
Circumference = 2p r = p d
Geometry Formulas
For a rectangular box of length L, width W, and
height H:
V o lu m e = lw h
For a sphere of radius r:
4 3
Volume = p r
3
Surface
Area = 4p r 2
For a right circular cylinder of height h and radius r:
2
Volume = p r h