Chapter 3- Groden Geometry Honors

Parallel lines

coplanar lines that do not intersect

Skew lines

non-coplanar lines

Parallel lines and planes

do not intersect

Parallel Planes

Planes that do not Intersect

Theorem

If two parallel planes are cut by a third plane then the lines of the intersection are parallel

Theorem

In a plane two lines perpendicular to the same line are parallel

Theorem

If two parallel lines are cut by a transversal then the alternate interior angles are congruent

Postulate

If two parallel lines are cut by a transversal then corresponding angles are congruent

Theorem

If two parallel lines are cut by a transversal then the same side interior angles are supplementary

Theorem

If a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other also

Postulate

If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel

Theorem

If two lines are cut by a transversal and the alternate interior angles are congruent then the lines are parallel

Theorem

If two lines are cut by a transversal and same side interior angles are supplementary then the lines are parallel

Theorem

Two lines parallel to a third line are parallel to each other

Triangle Definition

A figure formed by three segments joining three non-collinear points.

Auxiliary lines theorem

Through a point and and a line there is exactly one line parallel to the given line

Theorem

Through a point outside a line, there is exactly one line perpendicular to the given line

Theorem

The sum of the measures of the angles of a triangle is 180

Theorem

The measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles

Corollary one

If two angles of one triangle are congruent to two angles of another triangle then the third angles are congruent

Corollary two

Each angle of equilateral triangle has a measure of 60

Corollary three

In a triangle there can be at most one right angle or obtuse angle

Corollary four

The acute angles of a right triangle are complementary

Theorem

The sun of the measures of rain he angels of a convex polygon with n sides is (n-2)(180)

Regular polygon

a polygon that is both equilateral and equiangular

Theorem

The sun of the measures of the exterior angle of any convex polygon one angle at each vertex is 360