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19 Cards in this Set

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Theorem 11.1: Polygon Interior Angles Theorem.

The sum of the measures of the interior angles of a convex n-gon is...
(n-2) x 180
Corollary to Theorem 11.1

The measure of each interior angle of a regular n-gon is
(n-2) x 180
_____________

n
Theorem 11.2: Polygon Exterior Angles Theorem

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex is ____ degrees
360 degrees
Corollary to Theorem 11.2

The measure of each exterior angle of a regular n-gon is
1 360
_ x 360 or ______

n n
Theorem 11.3: Area of an Equilateral Triangle
The are of an equilateral trangle is one fourth the square of the length of one side times the square root of 3.

A= 1/4 x (SquareRoot)3 x s(squared)
Center of the polygon
The center of the polygon is the center of the circumscribed circle.
Radius of the polygon
The radius of the polygon is the radius of the circumscribed circle.
Apothem of the polygon
The distance from the center to any side of the polygon
Theorem 11.4: Area of a Regular Polygon
The area of a regular n-gon with side length s is half the product of the apothem a and the perimeter P

A= 1/2aP or 1/2a x ns
Central angle of a regular polygon
Central angle of a regular polygon is an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon.

360
Central angle: ____

# of sides
Theorem 11.5: Areas of Similar Polygons
If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is a(squared):b(squared)
Circumference
The circumference of a circle is the distance around the circle.
Theorem 11.6: Circumference of a Circle
The circumference C of a circle is C= pi(d) or C= 2(pi)r

D= Diameter R= Radius
Arc Length
An arc length is a portion of the circumference of a circle.
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 degrees.

Arc Length of AB mAB
________________ = _____

2(Pi)r 360

Arc Length of AB= mAB
_____x 2pi(r)
360
Theorem 11.7: Area of a Circle
The area of a circle is (pi) times the square of the radius

A= (pi)r(squared)
Sector of a Circle
A sector of a circle is the region bounded by two radii of the circle and their intercepted arc.
Theorem 11.8: Area of a Sector
A mAB
_ = _____

(pi)r2 360

A= mAB
____ x (pi)r2
360
Area of a Polygon
(Step by Step)
1. Find the perimeter by multiplying the side length by the number of sides
2. Find the degrees of the central angle by dividing 360 by the number of central angles.
3. Draw in apothem.
4. Divide central angle by 2.
5. Divide side length by 2.
6. Area = side length divided by the tangent of the (1/2)central angle.
7. Divide by two.