Geometry Theorems and Converses

2.1 Properties of Segment Congruence

Reflexive: For any segment AB, segment AB is congruent to segment AB.
Symmetric: If segment AB is congruent to segment CD, then segment CD is congruent to segment AB.
Transitive: If segment AB is congruent to segment CD and segment CD is congruent to segment EF, then segment AB is congruent to segment EF.

2.2 Properties of Angle Congruence

Reflexive: For any angle A, angle A is congruent to angle A.
Symmetric: If angle A is congruent to angle B, then angle B is congruent to angle A.
Transitive: If angle A is congruent to angle B and angle B is congruent to angle C, then angle A is congruent to angle C.

2.3 Right Angles Congruence Theorem

All right angles are congruent.

2.4 Congruent Supplements Theorem

If two angles are supplements to the same angle (or congruent angles), then the two angles are congruent.
If angles A and C and supplements and angles B and C are supplements, angles A and B are congruent.
If angles C and D are congruent and angles A and C and supplementary and angles B and D are supplementary, then angles A and B are congruent.

2.5 Congruent Supplements Theorem

If two angles are complements to the same angle (or congruent angles), then the two angles are congruent.
If angles A and C and complements and angles B and C are complements, angles A and B are congruent.
If angles C and D are congruent and angles A and C are complements and angles B and D are complements, then angles A and B are congruent.

2.6 Vertical Angles Congruence Theorem

Vertical angles are congruent.

3.1 Corresponding Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

3.2 Alternate Interior Angles Theorem

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

3.3 Alternate Exterior Angles Theorem

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

3.4 Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

3.5 Corresponding Angles Converse

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

3.6 Alternate Interior Angles Converse

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

3.7 Alternate Exterior Angles Converse

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

3.8 Consecutive Interior Angles Converse

If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.

3.9 Transitive Property of Parallel Lines

If two lines are parallel to the same line, then they are parallel to each other.
If line AB is parallel to line CD and line EF is parallel to line CD, then line AB is parallel to line EF.