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# Geometry Postulates and Theorems

From Geometry publish by Houghton Mifflin Company. Theroems 3-1 to 3-12 with Postulate 10 and 11.

AB
Theorem 3-1If two parallel planes are cut by a third plane, then the lines of intersection are parallel.
Theoroem 3-2If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Theorem 3-3If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.
Theroem 3-4If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.n
Theorem 3-5If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
Theorem 3-6If two lines are cut by a transversal and the same side interior angles are supplementary, then the lines are parallel.
Theorem 3-7In a plane, two lines perpendicular to the same line are parallel.
Theorem 3-8Through a point outside a line, there is exactly one line parallel to a given line.
Theorem 3-9Through a point outside a line, there is exactly one line perpendicular to the given line.
Theorem 3-10Two lines parallel to a third line, are parallel to each other.
Theorem 3-11The sum of the measures of the angles of a triangle is 180.
Theorem 3-12The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
Postulate 10If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Postulate 11If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

 Scott