# Geometry Postulates and Theorems

## 16 terms

### Right Angle Congruency Theorems

All right angles are congruent

### Congruent Supplement Theorem

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

### Congruent Complement Theorem

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

### Vertical Angles Theorem

If two angles are vertical angles, then they have equal measures.

### Theorem 3.1

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

### Theorem 3.2

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

### Theorem 3.3

If two lines are perpendicular, then they intersect to form four right angles.

### Alternate Interior Angles Theorem

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

### Consecutive Interior Angles Theorem

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

### Alternate Exterior Angles Theorem

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

### Perpendicular Transversal

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

### Alternate Interior Angles Converse

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

### Consecutive Interior Angles Converse

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

### Alternate Exterior Angles Converse

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

### Theorem 3.11

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

### Theorem 3.12

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.