3.1 Lines and Angles Unit IC Day 1

Do Now Parallel lines have _________ slopes. ◦ Give an example of a line that is parallel to y = -3x + 7 Perpendicular lines have ____________ slopes. ◦ Give an example of a line that is perpendicular to y = -3x + 7

Definitions Two lines are parallel if they are _____________ and do not _____________. Two lines are skew if they are not _____________ and do not _____________. Two planes are ____________ if they do not intersect.

Example 1: Identifying relationships in space Which segment(s) in the diagram appear(s) to fit the description? a. Parallel to AB and contains D b. Perpendicular to AB and contains D c. Skew to AB and contains D d. Name the plane(s) that contains D and appear to be parallel to plane ABE.

Postulate 13: Parallel Postulate If there is a line and a point not on the line, then _____________________ through the point, parallel to the given line. P l

Postulate 14: Perpendicular Postulate If there is a line and a point not on the line, then ___________________ through the given point, perpendicular to the given line. l P

Definitions: Transversal: a line that intersects two or more coplanar lines at different points. ________________: occupy corresponding positions. ◦ Examples: _______________: lie outside the two lines, on opposite sides of the transversal. ◦ Examples: _______________: lie between the two lines, on opposite sides of the transversal. ◦ Examples: ________________: lie between the two lines, on the same side of the transversal ◦ Examples:

Ex. 2: Identifying Angle Relationships List all of the pairs of angles that fit the description. a) Corresponding b) Alternate exterior c) Alternate interior d) Consecutive interior

Perpendicular Construction 1. Draw a line ℓ and a point P not on ℓ. 1. Place the compass at point P and draw an arc that intersects the line ℓ twice. Label the intersections A and B. 1. Place the compass at point A and draw an arc. Using the same radius, place the compass at point B and draw another arc. Label the intersection of the arcs Q. 1. Use a straight edge to draw PQ.

Closure If two lines are cut by a transversal, how many pairs of corresponding angles are formed?