Chapter 3: Perpendicular and Parallel Lines Section 3.1: Lines and Angles

parallel lines – two lines that are coplanar and do not intersect. skew lines – lines that do not intersect and are not coplanar.

parallel planes – two planes that do not intersect.

Parallel and Perpendicular Postulates Postulate 13: Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. P

Postulate 14: Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. p

transversal – a line that intersects two or more coplanar lines at different points.

corresponding angles – two angles that occupy the same corresponding positions.

alternate exterior angles – two angles are alternate exterior angles if they lie outside the two lines on opposite sides of the transversal.

alternate interior angles – two angles are alternate interior angles if they lie between the two lines on opposite sides of the transversal.

consecutive interior angles – angles that lie between the two lines on the same side of the transversal. Also called same side interior angles. Angles 3 and 5 Angles 4 and 6

Example 1: List all pairs of angles that fit the description

a)Corresponding 1 and 3 2 and 4 5 and 7 6 and 8

b) Alternate exterior 1 and 8 4 and 5 c)Alternate interior 2 and 7 3 and 6 d)Consecutive interior 2 and 3 6 and 7

Example 2: Find the measures of all of the angles. 110°

Example 3: Think of each segment in the diagram as part of a line. Which of the lines appear to fit the description? Q R P S U V T W

a)Parallel to TW and contains V Line UV b)Perpendicular to TW and contains V Line VW c)Skew to TW and contains V Lines RV and SV d)Name the plane(s) that contain V and appear to be parallel to plane TPQ. plane RVW

HOMEWORK pg. 132 – 133; 6 – 17,