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Geometry Postulates and Theorems

Chapter 3
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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.