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# Part 2

 Postulate 9 For any two points, there is exactly one line containing them. Theorem 2.5 Two lines intersect at exactly one point. Postulate 10 If two points of a line are in a given plane, then the line itself is in the plane. Theorem 2.6 If a line intersects a plane, but is not contained in the plane, then the intersection is exactly one point. Postulate 11 If two planes intersect, then they intersect in exactly one line. Postulate 12 Three noncollinear points are contained in exactly one plane. Theorem 2.7 A line and a point not on the line are contained in exactly one plane. Theorem 2.8 Two intersecting lines are contained in exactly one plane. Postulate 13 Alternate Interior Angles Postulate: If a transversal intersects two lines such that alternate interior angles are congruent (equal in measure), then the lines are parallel. Theorem 3.1 If a transversal intersects two lines such that corresponding angles are congruent, then the lines are parallel. Theorem 3.2 If two lines are intersected by a transversal such that interior angles on the same side of the transversal are supplementary, then the lines are parallel. Theorem 3.3 In a plane, if two lines are perpendicular to the same line, then they are parallel. Theorem 14 Parallel Postulate: Through a point not on a line, there is exactly one line parallel to the given line. Theorem 3.4 If two parallel lines are intersected by a transversal, then alternate interior angles are congruent. Theorem 3.5 If two parallel lines are intersected by a transversal, then corresponding angles are congruent. Theorem 3.6 If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are supplementary. Theorem 3.7 If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. Theorem 3.8 In a plane, if two lines are parallel to the line, then they are parallel to each other. Theorem 3.9 The sum of the measures of the angles of a triangle is 180. Theorem 3.10 Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. Theorem 3.11 If two parallel planes are intersected by a third plane, then the lines of intersection are parallel.

Note: The concepts in this collection may not be entirely accurate.
They are for reference only.