## Theorems

August 18, 2023

If two lines intersect, then they intersect at exactly one point.

If there is a line and a point not on the line, then exactly one plane contains them.

If two lines intersect, there exists exactly one plane to contain them.

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

If two lines in a plane are perpendicular to the same line. then they are parallel to each other.

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other one.

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

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

All right angles are congruent.

If two lines are parallel to the same line, then they are parallel to one other.

If two angles are complementary to the same angle or to congruent angles, then they are congruent.

If two angles are supplementary to the same angle or to congruent angles, then they are congruent.

If two angles form a linear pair, then they are supplementary.

Vertical Angle Theorem If two angles are vertical angles, then they are congruent.

If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.

If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.

If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.

If a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle.

If there is a line and a point not on the line, then exactly one plane contains them.

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

If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel.

If two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, the lines are parallel.