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# Basic Geometry Formulas

A quadrilateral is a four-sided polygon. A paralle logram , a rectangle, a square, a rhombus, and a trapezoid are all quadrilaterals.

A circle is a plane figure in which all points are the same distance from the center of the circle. A diameter of a circle is a line segment across the circle through the center. A radius of a circle is a line segment from the center of the circle to a point on the circle.

The perimeter of a plane geometric figure is a measure of the distance around the figure. The distance around a circle is called the circumference. Area is the amount of surface in a region. Volume is a measure of the amount of space inside a figure in space. The surface area of a solid is the total area on the surface of the solid.

When calculating perimeter of composite figures Be Careful!!!!! In most cases, when calculating the perimeter of a composite figure, you have to deduct one of the sides in your formulas. If you don’t, you’ll end up calculating the same side.

Essential Rules

Triangle
Sum of the measures of the interior angles = 180°
Sum of an interior and corresponding exterior angle = 180°
Rules to determine congruence: SSS Rule, SAS Rule, ASA Rule

Perimeter

 Triangle: P = a + b + c Rectangle: P = 2L + 2W Square: P = 4s Circle: C = πd or C = 2πr

Area

 Triangle: A = 1/2bh Rectangle: A = LW Square: A = s2 Circle: A = πr2 Parallelogram: A = bh Trapezoid A = 1/2h (b1 + b2)

Volume

 Rectangular solid: V = LWH Cube : V = s3 Sphere: V = (4/3)πr3 Right circular cylinder: V = πr2h Right circular cone: V = (1/3) πr2h Regular pyramid: V = (1/3)s2h

Surface Area

 Rectangular solid: SA = 2LW + 2LH + 2WH Cube: SA = 6s2 Sphere: SA = 4 πr2 Right circular cylinder: SA = 2 πr2 + 2 πrh Right circular cone: SA = πr2 + πrl Regular pyramid: SA = s2 + 2sl Trapezoid SA = (b1 + b2)h + pH (H = length of the longest base)

Pythagorean Theorem

It can be used to find the length of the sides of a triangle and the distance or height between two points . If a and b are the legs of a right triangle and c is the length of the hypotenuse, then a2 + b2 = c2

Principal Square Root Property
If r2 = s, then r = , and r is called the square root of s .

Similar Triangles
The ratios of corresponding sides are equal. The ratio of corresponding heights is equal to the ratio of corresponding sides.

< 1 = < 4 and < 3 = < 5 because they are alternate interior angles

Circle
The measure of an arc equals the measure of the central angle.
Arc length = measure of central angle circumference

Measure of central angle =

The central angle is < ABC. The arc is AC

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