Geometry Unit 3 Postulates and Theorems

Same-Side Interior Angles Postulate

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

Alternate Exterior Angles Theorem

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

Alternate Interior Angles Theorem

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

Corresponding Angles Theorem

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

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.

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.

Converse of the Corresponding Angles Theorem

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

Converse of the Same-Side Interior Angles Postulate

If two lines and a transversal form sameside interior angles that are supplementary, then the two lines are parallel.

Perpendicular Transversal Theorem

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

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.

In a plane, if two lines are perpendicular to the same line,

then they are parallel to each other.

Triangle Angle-Sum Theorem

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