Geometry Theorems

Right Angle Theorem

If 2 angles are right, then they are congruent.

Straight Angle Theorem

If 2 angles are straight, then they are congruent.

Addition (3)

If a segment/angle is added to a pair of congruent segments/angles, then the resulting segments/angles are congruent.

Addition (4)

If two segments/angles are added to a pair of congruent segments/angles, then the resulting segments/angles are congruent.

Subtraction (3)

If a segment/angle is subtracted from a pair of congruent segments/angles, then the resulting segments/angles are congruent.

Subtraction (4)

If two segments/angles are subtracted from a pair of congruent segments/angles, then the resulting segments/angles are congruent.

Multiplication

If two segments or angles are congruent, then their like (2 or 3) multiples are also congruent.

Division

If two segments or angles are congruent, then their like (2 or 3) divisions are also congruent.

Complementary (3)

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

Complementary (4)

If two angles are complementary to a pair of congruent angles, then they are congruent.

Supplementary (3)

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

Supplementary (4)

If two angles are supplementary to a pair of congruent angles, then they are congruent.

Transitive (3)

If two segments/angles are congruent to the same segment/angle, then they are congruent.

Transitive (4)

If two segments/angles are congruent to a pair of congruent segments/angles, then they are congruent.