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Basic Geometry Formulas
Basic Geometry Formulas
A quadrilateral is a foursided 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 = s^{2} 
Circle:  A = πr^{2} 
Parallelogram:  A = bh 
Trapezoid  A = 1/2h (b_{1} + b_{2}) 
Volume
Rectangular solid:  V = LWH 
Cube :  V = s^{3} 
Sphere:  V = (4/3)πr^{3} 
Right circular cylinder:  V = πr^{2}h 
Right circular cone:  V = (1/3) πr^{2}h 
Regular pyramid:  V = (1/3)s^{2}h 
Surface Area
Rectangular solid:  SA = 2LW + 2LH + 2WH 
Cube:  SA = 6s^{2} 
Sphere:  SA = 4 πr^{2} 
Right circular cylinder:  SA = 2 πr^{2} + 2 πrh 
Right circular cone:  SA = πr^{2} + πrl 
Regular pyramid:  SA = s^{2} + 2sl 
Trapezoid  SA = (b_{1} + b_{2})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 a^{2} + b^{2} = c^{2}
Principal Square Root Property
If r^{2} = 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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