1. 1. Name a line that does not intersect AD.
ANSWER BC
2. What is the intersection of AD and DB?
ANSWER D

2. 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.

3. 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

4. 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.

5. VOCABULARY
Regarding two lines cut by a transversal…
Corresponding angles
1 and 5, and 6,
3 and 7, and 8
Alternate interior angles
2 and 7, and 5
Alternate exterior angles
1 and 8, and 6
Consecutive interior angles
2 and 5, and 7

6. 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.

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? b.
Line(s) skew to CD and containing point A
SOLUTION
Both AG and AH appear skew to CD and contain point A. b.

8. 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.

9. 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.

10. 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

11. 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

12. GUIDED PRACTICE
for Example 3
Classify the pair of numbered angles. 3.
ANSWER
corresponding angles

13. GUIDED PRACTICE
for Example 3
Classify the pair of numbered angles. 4.
ANSWER
alternate exterior angles.

14. GUIDED PRACTICE
for Example 3
Classify the pair of numbered angles. 5.
ANSWER
alternate interior angles.