GeometrySection 3.1

Identify Pairs of Lines and Angles

Postulates1. Through any two points there exists

exactly one line2. A line contains at least two points3. If two lines intersect, then their

intersection is exactly one point.

Postulates1. Through any three noncollinear points

there exists exactly one plane. 2. A plane contains at least three

noncollinear points3. If two points lie in a plane, then the line

containing them lies in the plane.4. 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

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

8

7

Name the Angles!!

1

23

4

56

7 8

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

32, 40-42