Planes & Polygons

ways to determine a plane

• three non-collinear points

• a line and a point not on the line

• two intersecting lines

• two parallel lines

Line Plane Intersect Postluate

If a line intersects a plane not containing it, then the intersection is exactly one point

Two Plane Intersection

If two planes intersect, their intersection is exactly one line

Line perpendicluar to a Plane

A line is perpendicular to a plane, if it is perpendicular to every line in the plane that passes through the intersection point

Line Perpendicular Therom

If a line is perpendicular to two intersecting lines that lie in a plane, then it is perpendicular to the plane

Parallel Line and Plane Definition

A line and a plane are parallel if they do not intersect

Two Plane Parallel Definition

Two planes are parallel if they do not intersect (No Skew Planes!)

Two Skew Lines Definition

Two lines of Skew if they are not coplanar

Plane Intersecting two Parallel Planes Therom

If a plane intersects two parallel planes, then the lines of the intersection are parallel

Two Planes and Perpendicular line

If two planes are perpendicular to the same line, then they are parallel to each other

Two Planes and Perpendicular Line 2

If a line is perpendicular to one of two parallel planes, then it is perpendicular to the other plane as well.

Three Planes, Two Parallel

If two planes are parallel to the same plane, then they are parallel to each other.

Two Perpendicluar Lines and One Plane

If two lines are perpendicular to the same plane, then they are parallel to each other.

Two Parallel Lines, One Perpendicular in the Plane

If a plane is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well.

Exterior Angle Definition

An angle that is adjacent and supplementary to an interior angle of a polygon

Exterior Angle Therom

The measure of an exterior angle of a triagle is equal to the sum of hte measures of the two remote interior angles

Midline Definition

A segment joining the midpoints of two sides of a triangle

Midline Theorem

The midline of a triangle is parallel to the third side and its length is half of the third side

Regular Polygon Definiton

A regular polygon is a covex polygon with all sides cogruent and all angles congruent

Sum of interior angles of a polygon

180 * n-2 (n=number of sides + works with all polygons)

Measure of one interior angle

180 * n-2 / n

Sum of Exterior Angles of a Polygon

360

Measure of one Exterior Angle

360/n (only regular polygons)

Convex Polygons

No interior angler greater than 180

Concave Polygon

At least one interior angle is greater than 180

decagon, hendeacgon, dodecagon

ten sides, eleven sides, twelve sides

pentagon, hexagon, heptagon

five sides, six sides, seven sides

Number of triangles formed

n - 2