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
