Download Chapter 8 Notes - Kenston Local Schools

Chapter 8 Notes
Convex and Non-Convex Polygons
A polygon is a closed figure made up of straight line segments connected end-to-end. These
segments may not cross (intersect) at any other points.
A regular polygon is equilateral and equiangular (all sides have the same length the interior
angles have equal measure). The example is a regular hexagon- all sides have the same
length and each interior angle has the same measure.
A polygon is called convex if you can connect the vertices without
leaving the inside of the shape.
Examples:
Convex
Non convex
Interior Angles of a Polygon
•
The sum of the measures of the interior angles of an n-gon is 180(n - 2).
"n" represents the number of sides.
•
The measure of each angle in a regular n-gon
180°0/
Exterior Angles of a Polygon
•
The sum of the exterior angles of an n-gon is always 360°.
•
The measure of each exterior angle in a regular n-gon is :
is: .
Special Quadrilateral Properties
Parallelogram:
Opposite sides of a parallelogram are congruent and parallel.
Opposite angles are congruent.
The diagonals create two pair of congruent triangles.
The diagonals bisect each other.
Rhombus:
It has all of the properties of a parallelogram.
Plus its diagonals are perpendicular bisectors and bisect the
angles of the rhombus.
The diagonals create four congruent triangles.
Rectangle:
It has all of the properties of a parallelogram.
In addition, its diagonals must be congruent.
Isosceles Trapezoid:
The base angles (angles joined by a base) of an isosceles
trapezoid are congruent.
Ratios of Similarity
We have looked at the ratios of triangles before to
see if triangles are similar. This can also be called
a ratio.
For example, notice that the two triangles are similar
because of AA -. Since the corresponding sides of
the original and new shape are 6 and 9, it can be
6
stated that r = -9
2
-3oratif
Circle Facts
The area of a circle with radius
r=
1 unit is
u
unite. (Remember that
u=
3.1415926...)
Area = itr2
Circumference = 2ffr rut
All circles are similar The area is it r2
The circumference of a circle is its perimeter. It is the distance around a circle.
arc
A part of a circle is called an arc. This is a set of points a fixed distance from a
center and is defined by a central angle. Since a circle does not include its
interior region, an arc is like the edge of a crust of a slice of pizza.
A region that resembles a slice of pizza is called a sector. It is formed by two radii
of a central angle and the arc between their endpoints on the circle.
Arc Length and Area of a Sector
To find the area of a sector, set up a proportion:
area of the sector
area of the entire circle
_ measurement
of
central angle
360.
Example:
To find the length of an arc, set up a dfferent proportion
arc length
circumference of circle
Example:
measurement
of
central angle
360°
sector
)