Identify Pairs of Lines and Angles Geometry Section 3.1 Identify Pairs of Lines and Angles

Postulates Through any two points there exists exactly one line A line contains at least two points If two lines intersect, then their intersection is exactly one point.

Postulates Through any three noncollinear points there exists exactly one plane. A plane contains at least three noncollinear points If two points lie in a plane, then the line containing them lies in the plane. If two planes intersect, then their intersection is a line.

Angle Theorems and Postulates Right angles congruence theorem All right angles are congruent Linear Pair Postulate If two angles form a linear pair, then they are supplementary Vertical Angles Congruence Theorem Vertical angles are congruent

Two coplaner lines that do not intersect are called parallel lines Two lines are skew lines if they do not intersect and are not coplaner Two planes that do not intersect are parallel planes

Line Postulates Parallel postulate Perpendicular postulate If there is a line and a point not on the line, there is exactly one line through that point that is parallel to the given line. Perpendicular postulate If there is a line and a point not on the line, there is exactly one line through that point that is perpendicular to the given line.

Angles formed by Transversals A transversal is a line that intersects two ore more coplaner lines at different points. Corresponding angles have corresponding positions 1 2

Alternate interior angles are between the two lines, and on opposite sides of the transversal 3 4

Alternate exterior angles lie outside the two lines and on opposite sides of the transversal 5 6

Consecutive interior angles lie between the two lines on the same side of the transversal 7 8

Name the Angles!! 3 2 1 4 5 6 7 8

Assignment Section 3.1 Page 150 Problems # 4-10 even, 11-14, 18-23, 24-32, 40-42