A **theorem** is a mathematical statement that has been proven. It can be used in proofs.

## List of Theorems that can be Used in Proofs

If two angles are right angles, then they are congruent.

If two angles are straight angles, then they are congruent.

If a point, ray, or line divides a segment into two congruent segments, it bisects the segment.

If two points, rays, or lines divide a segment into three congruent segments, it trisects the segment. Angle Addition Postulate- (Two little angles next to each other add up to form one big angle)

If two angles add up to 90 degrees, they are complimentary.

If two angles add up to 180 degrees, they are supplementary.

If two angles are complimentary to congruent angles, then they are congruent.

If two angles are supplementary to congruent angles, then they are congruent.

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

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

Perpendicular lines form right angles.

Addition Property of Congruence- (If two congruent angles or sides have the same numerical increments, they are congruent)

Subtraction Property of Congruence- (If two congruent angles or sides have the same numerical decrements, they are congruent)

Multiplication Property of Congruence- (If two congruent angles or sides are multiplied by the same number, they are congruent)

Division Property of Congruence- (If two congruent angles or sides are divided by the same number, then they are congruent)

Transitive Property- (If segments or angles are congruent to the same segment or angle they are congruent to each other)

Substitution Property- (Like the Transitive Property, but instead it substitutes in congruent angles with complimentary and supplementary)

Reflexive Property- (For any real numbers, a=a. For any segment AB=AB. For any angle m<a=m<a)

Perpendicular lines form right angles.

Lines, rays, or segments that intersect at right angles are perpendicular.

Vertical angles are congruent.

Side-Side-Side- The triangles are congruent because all of their sides are congruent with both triangles.

Angle-Angle-Side- The triangles are congruent because two angles and one side are congruent with both triangles.

Side-Angle-Side- The triangles are congruent because two sides and one angle are congruent with both triangles.

Angle-Side-Angle- The triangles are congruent because two angles with a side in between are congruent with both triangles.

Hypotenuse-Leg- Right triangles are congruent if the hypotenuse and leg are congruent with both triangles.

Corresponding parts of congruent triangles are congruent.

The altitude of a triangle forms right angles to the side to which it is drawn.