# Geometry Postulates and Theorems

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Chapter 3

### Postulate 3-1 Corresponding Angles Postulate

If a transversal intersects two parallel lines, then corresponding angles are congruent

### Theorem 3-1 Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternate interior angles are congruent

### Theorem 3-2 Same-Side Interior Angles Theorem

If a transversal intersects two parallel lines, then same-side interior angles are supplementary.

### Theorem 3-3 Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then alternate exterior angles are congruent

### Postulate 3-2 Converse of the Corresponding Angles Postulate

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel

### Theorem 3-4 Converse of the Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel

### Theorem 3-5 Converse of the Same-Side Interior Angles Theorem

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel

### Theorem 3-6 Converse of the Alternate Exterior Angles Theorem

If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel

### Theorem 3-7

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

### Theorem 3-8

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

### Theorem 3-9 Perpendicular Transversal Theorem

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

### Postulate 3-3 Parallel Postulate

Through a point not on a line, there is one and only one line parallel to the given line

### Theorem 3-10 Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180

### Theorem 3-11 Triangle Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles

### Postulate 3-4 Perpendicular Postulate

Through a point not on a line, there is one and only one line perpendicular to the given line.

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