Geometry Chapter 11
Area of a Square Postulate
The area of a square is the square of the length of its side.
Area Congruence Postulate
If two polygons are congruent, then they have the same area.
Area Addition Postulate
The area of a region is the sum of the areas of its non-overlapping parts.
Area of a Rectangle Theorem
The area of a rectangle is the product of its base and height.
Area of a Parallelogram Theorem
The area of a parallelogram is the product of a base and its corresponding height.
Area of a Triangle Theorem
The area of a triangle is one half the product of a base and its corresponding height.
height (of a trapezoid)
the perpendicular distance between its bases
Area of a Trapezoid Theorem
The area of a trapezoid is one half the product of the height and the sum of the lengths of its bases.
Area of a Rhombus or a Kite Theorem
The area of a rhombus or a kite is one half the product of the lengths of its diagonals.
Areas of Similar Polygons Theorem
If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is a²:b².
Circumference of a Circle Theorem
The circumference C of a circle is C=πd or C=2πr where d is the diameter and r is the radius of the circle.
C=πd or C=2πr
Arc Length Corollary
In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360°.
(Arc length of AB/πd) = (mAB/360°)
Area of a Circle Theorem
The area of a circle is π times the square of the radius. A=πr²
Area of a Sector Theorem
The ratio of the area of a sector of a circle to the whole circle (πr²) is equal to the ratio of the measure of the intercepted arc to 360°.
(Area of sector APB/πr²) = (mAB/360°)
center (of the polygon)
center of its circumscribed circle
radius (of the polygon)
radius of its circumscribed circle
apothem (of the polygon)
the distance from the center to any side of the polygon
is the height to the base of an isosceles triangle that has two radii as legs
central angle (of a regular polygon)
any angle formed by two radii drawn to consecutive vertices of the polygon
central angle equation
360°/number of sides
Area of a Regular Polygon Theorem
Area of a regular n-gon with side length s is half the product of the apothem a and the perimeter P.
A=½∗a∗P or A=½∗a∗n∗s
probability (of an event)
measure of the likelihood that the event will occur
a number between 0 & 1, inclusive
can be expressed as a fraction, decimal, or percent
ratio that involves a geometric measure such as length or area