Polygon
Simple, closed figure formed by 3 or more coplanar line segments (sides); sides meet at vertices
Concave
Polygon that contains a reflex angle (greater than 180 degrees)
Convex
Polygon that contains angles that are NOT reflex angles (acute, obtuse, or right angles only)
Regular Polygon
Polygon that is equilateral and equiangular
Sum of Interior Angles of a Polygon
Given a convex n-gon, it is (n-2)180
Sum of Exterior Angles of a Polygon
Given a convex n-gon, it is 360 degrees
Measure of Interior Angle of a Regular Polygon
Given a regular n-gon, it is ((n-2)180)/n;
alternatively, 180 - measure of exterior angle
Diagonal
Line segment that connects two nonconsecutive vertices of a polygon
Parallelogram
A quadrilateral with:
opposite sides parallel;
opposite sides congruent;
opposite angles congruent;
consecutive angles supplementary;
diagonals bisect each other;
diagonals form two congruent triangles
Rectangle
A parallelogram with:
4 right angles;
diagonals are congruent
Rhombus
A parallelogram with:
4 congruent sides;
diagonals bisect angles;
diagonals are perpendicular
Square
A parallelogram that is both a rectangle and rhombus:
4 right angles;
diagonals congruent;
4 congruent sides;
diagonals bisect each other;
diagonals are perpendicular
Trapezoid
A quadrilateral with OAOO pair of parallel sides;
the parallel sides are called the bases,
the non-parallel sides are the legs
Isosceles Trapezoid
A trapezoid with congruent legs (the non-parallel sides are congruent);
base angles are congruent;
diagonals are congruent;
opposite angles are supplementary;
midsegment is parallel to the bases and its length is half the sum of the bases
Kite
A quadrilateral with 2 pairs of consecutive congruent sides, but opposite angles are not congruent;
has OAOO set of congruent opposite angles (the angles between the non-congruent sides);
diagonals are perpendicular
Measure of Exterior Angle of a Regular Polygon
Given a regular n-gon, it is 360/n