Chapter 8 Flashcards
convex
a poygon is convex if no line that contains a side of the polygon passes through the interior of the polygon.
concave
a polygon that is not convex is called concave
equilateral
a polygon where all of its sides are congruent
equiangular
a polygon where all of its interior angles are congruent
regular
a polygon where both it is both equilateral and equiangular
Theorem 8.1 “polygon interior angles theorem”
The sum of the measure of the interior angles o fa convex polygon with n sixes is (n - 2) of 180`
8.2 Theorem “Polygon exterior angles theorem”
The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360`
Area
the amount of surface covered by a figure
Area of a square
A = (side)^2
Area of a rectangle
Area = (base)(height)
height of a triangle
the perpendicular segment from a vertex to the line containing the opposite side.
base of the triangle
the opposite side of the of the perpendicular segment
Area of a triangle
Area = 1/2(base)(height)
Theorem 8.3 “Areas of similar polygons”
If two polygons are similar with a scale factor of a/b, then the ratio of their areas is a^2 over b^2
bases of a parallelogram
either pair of parallel sides of a parallelogram
height of a parallelogram
the shortest distance between the bases of a parallelogram
the segment that represents the heights is perpendicular to the bases.
Area of a parallelogram
Area = (base)(height)
Area of a rhombus
Area = 1/2(product of diagonals)
height of the trapezoid
the shortest distance between the bases
Area of a trapezoid
Area = 1/2(height)(sum of bases)
Circle
the set of all points in a plane that are the same distance from a given point
Center
the set of all points in a plane that are the same distance from a given point, this is the center
radius
the distance from the center to a point on the circle
diameter
the distance across the circle, through the center
circumference
the distance around the circle
Circumference of a circle
Circumference = 3.14 of diameter or 2 of 3.14 of radius
Area of a circle
Area = 3.14(radius)^2
central angle
an angle whose vertex is the center of a circle
sector
a region of a circle determined by two radii and a part of the circle
Area of secter measure of central angle
————————— = —————————————
Area of entire circle measure of entire circle
