Chapter 8

8.1- Classifying Polygons

A polygon is a plane figure formed by three or more segments called sides
A polygon is a convex if no line that contains a side of the polygon that passes through the interior of the polygon
A polygon is a concave if at least one line that contains a side of the polygon that passes through the interior of the polygon
A polygon that is not convex is called concave
A polygon is equilateral if all its sides are congruent
A polygon is equiangular if all its angles are congruent
A polygon is regular if it is both equilateral and equiangular

8.2- Interior and Exterior Angle Theorem

Polygon Interior Angle Theorem- If the sum of the measures of the interior angles of a convex polygon with N sides is ( n-2) x 180 degrees

Symbols- m<1 + m<2 + m<... = (n-2) x 180 degrees

Polygon Exterior Angle Theorem- The sum of the measures of the exterior angles of a convex polygon, K at each vertex is 360

Symbols- m<1 + m<2 + m<... +m<n = 360

8.3- Are of Squares and Rectangles

The amount of area surfaced by a figure is called the area

Area= (side) squared
A=s squared

Area of a rectangle-

Area- (base)(height)
A= bh

Area of a complex polygon- to find the area of <CP, divide the polygon into smaller polygons whose areas you can find

8.4- Area of Triangles

The height and base of a triangle are used to find its Area.

The height of a triangle is the perpendicular segment from a vertex to the line containing the opposite side.

The base of a triangle is the side opposite the height.

Triangles can have the same area but not be congruent.

Area of a Triangle- Area = ½ bh

In a right triangle a leg is a height

A height can be inside a triangle

A height can be outside a triangle 

Area of Similar Polygons Theorem- If two polygons are similar with a scale factor of a/b, then the ratio of their areas is a squared/ b squared.

Symbols: If ABCD is similar to EFGH with a scale factor of a/b then Area of ABCD/ Area of EFGH= a squared/ b squared

8.5-Area of Parallelograms and Rhombi

Either pair of parallel sides of a parallelogram are called the bases of the parallelogram.

The shortest distance between the bases of a parallelogram is called the height of a parallelogram.

The height of a parallelogram is perpendicular to the bases.

Area of a Parallelogram- A=bh

A height can be inside a parallelogram

A height can be outside a parallelogram

Are of a Rhombus- ½ d1 d2 (product of diagonals)

Or you could always divide the Rhombus into four congruent triangles

8.6- Area of Trapezoids

The shortest distance between the bases of a trapezoid is called the height of a trapezoid

Recall the area of a trapezoid- 1/2 (b1 + b2)

The area of a parallelogram- bh

1/2 height (sum of bases)

8.7- Circumference and Area of Circles Pie

Circle- set of all point in a plane that are the same distance from a given pout, called the center of the circle

Center- given point, a circle with the center P is called "circle p," OR (CIRCLE SYMBOL) p

Radius- distance from the center to a point on the  circle, plural= radii

Diameter- distance  across the circle, through the center

Circumference- distance around the circle

Central Angle- angle whose vertex is the center of a circle

Sector- A of a sector/ A of the circle= m< central angle/ 360 degrees