1. Name a line that does not intersect AD. ANSWER BC 2. What is the intersection of AD and DB? ANSWER D
Use Properties of Parallel and Perpendicular Lines Target Use Properties of Parallel and Perpendicular Lines You will… Identify angle pairs formed by three intersecting lines.
VOCABULARY parallel lines – two coplanar lines that do not intersect skew lines – two noncoplanar lines that do not intersect parallel planes – two planes that do not intersect transversal – a line that intersects two or more coplanar lines at different points
VOCABULARY Parallel Postulate 13 – 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. Perpendicular Postulate 14 – 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.
VOCABULARY Regarding two lines cut by a transversal… Corresponding angles 1 and 5, 2 and 6, 3 and 7, 4 and 8 Alternate interior angles 2 and 7, 4 and 5 Alternate exterior angles 1 and 8, 3 and 6 Consecutive interior angles 2 and 5, 4 and 7
EXAMPLE 1 Identify relationships in space Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description? a. Line(s) parallel to CD and containing point A SOLUTION AB , HG , and EF all appear parallel to CD , but only AB contains point A. a.
EXAMPLE 1 Identify relationships in space Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description? b. Line(s) skew to CD and containing point A SOLUTION Both AG and AH appear skew to CD and contain point A. b.
EXAMPLE 1 Identify relationships in space Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description? c. Line(s) perpendicular to CD and containing point A SOLUTION c. BC, AD , DE , and FC all appear perpendicular to CD , but only AD contains point A.
EXAMPLE 1 Identify relationships in space Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description? d. Plane(s) parallel to plane EFG and containing point A SOLUTION d. Plane ABC appears parallel to plane EFG and contains point A.
GUIDED PRACTICE for Examples 1 and 2 1. Look at the diagram in Example 1. Name the lines through point H that appear skew to CD. ANSWER AH , EH
EXAMPLE 3 Identify angle relationships Identify all pairs of angles of the given type. a. Corresponding b. Alternate interior c. Alternate exterior Consecutive interior d. SOLUTION a. ∠ 5 1 and ∠ 6 2 ∠ 7 3 ∠ 8 4 b. ∠ 7 2 and ∠ 5 4 d. ∠ 5 2 and ∠ 7 4 c. ∠ 8 1 and ∠ 6 3
GUIDED PRACTICE for Example 3 Classify the pair of numbered angles. 3. ANSWER corresponding angles
GUIDED PRACTICE for Example 3 Classify the pair of numbered angles. 4. ANSWER alternate exterior angles.
GUIDED PRACTICE for Example 3 Classify the pair of numbered angles. 5. ANSWER alternate interior angles.