Vertical angles are two angles whose sides form two pairs of opposite rays. When two lines intersect, two pairs of vertical angles are formed.

Theorem:

Vertical angles are congruent:

Perpendicular Lines:( ^ means perpendicular)

Perpendicular lines are two lines that form right angles.

Theorem:

Adjacent angles formed by perpendicular lines are congruent.

Theorem:

If two lines form congruent adjacent angles, then the lines are perpendicular.

Theorem:

If the exterior sides of two adjacent acute angles are perpendicular then the angles are complementary.

Theorem:

If two angles are supplements of congruent angles ( or of the same angle), then the two angles are congruent.

Theorem:

If two angles are complements of congruent angles ( or of the same angle), then the two angles are congruent.

Postulate:

A line contains at least two points, a plane contains at least three points but not all in one line, and space contains at least four points, but not all on one plane.

Postulate:

Through any two points, there is exactly one line.

Postulate:

Through any three points, there is at least one plane, and through any three noncollinear point there is exactly one plane.

Postulate:

If two points are in a plane then the line through the points are in that plane.

Postulate:

The intersection of two planes is a line.

Theorem:

The intersection of two lines is exactly at one point.

Theorem:

If line and a point not on the line exist, then a plane contains both
figures.

Theorem:

If two lines intersect, then a plane contains both of them.