Download Chapter 11 Notes

Chapter 11 Notes
Section 11.1
• Polygon Interior Angles Theorem: The sum of the measures of the interior angles of
a convex n-gon is (n  2)  180 where n is the number of sides.
• Corollary: The measure of each interior angle of a regular n-gon is
1
(n  2)
 (n  2)  180 or
 180
n
n
• Polygon Exterior Angles Theorem: The sum of the measures of the exterior angles
of a convex polygon, one angle at each vertex, is 360
• Converse: The measure of each exterior angle of a regular n-gon is
1
360
 360 or
.
n
n
Section 11.2
• Area of an Equilateral Triangle: The area of an equilateral triangle is one fourth the
square of the length of the side times
3. A 
1
1
3 s 2 or s 2
4
4
3.
• The center of a polygon and radius of a polygon are the center and radius of its
circumscribed circle, respectively.
• Apothem The apothem of a polygon is the distance from its center to any side.
• Central Angle: The central angle of a regular polygon is an angle whose vertex is the
center and whose sides contain two consecutive vertices of the polygon.
• 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, so A 
1
1
aP or A  a  ns.
2
2
Section 11.3
• 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 2  b 2 .
Side length of Quad . I
a
 .
Side length of Quad . II b
Section 11.4
• Circumference: is the distance around a circle.
• Circumference of a Circle: The circumference C of a circle is C  2 r , or C   d
where d is the diameter and r is the radius of the circle.
• 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 .
Arc length of AB m AB

,
2 r
360
or Arc length of AB 
m AB
 2 r
360
Section 11.5
• Area of a Circle: The area of a circle is  times the radius, or A   r 2 .
• Area of a Sector: The ratio of the area A of a sector of a circle to the area of the circle
is equal to the ratio of the measure of the intercepted arc to 360 .
A
mAB
mAB

, or A 
  r2
2
r
360
360
Section 11.6
• Probability: A number from 0 to 1 that represents the chance that an event will occur.
• Probability and Length: Let AB be a segment that contains the segment CD . If a
point K on AB is chosen at random, then the probability (P) that it is on CD is as
Length of CD
follows: P (Point K is on CD ) =
A C D
B
Length of AB.
• Probability and Area: Let J be a region that contains region M. If a point K in J is
chosen at random, then the probability that it is in region M is as follows:
Area of M
P(Point K is in region M) =
.
Area of J