1. Geometry Bellwork 9/16/14

2. Lines that do not intersect and are coplanar. Lines m and n.
Section 3.1
Identify Pairs of Lines and Angles
Key Concepts:
Diagram
Parallel lines:
Skew lines:
Parallel planes:
Lines that do not intersect and are coplanar.
Lines m and n.
Lines that do not intersect and are NOT coplanar.
Lines m and k.
Planes that do not intersect.
Planes T and U.

3. EXAMPLE 1
Identify relationships in space
Think of each segment in the figure as part of a line. Complete the statements. a.
Name the 3 lines parallel to CD .
AB , HG, EF b.
Name the 4 lines perpendicular to AH .
HG , EH , AB, DA c.
Name the 5 lines skew to ED.
HG, FG, AB, CB, AG d.
Is plane EFG parallel, skew, or perpendicular to plane CFG?
perpendicular

4.   parallel perpendicular oblique Section 3.1
Identify Pairs of Lines and Angles
PARALLEL AND PERPENDICULAR LINES Two lines that are in the same plane are either __________( ), ___________________ ( ), or ___________.
parallel 
perpendicular
oblique 
parallel
perpendicular
oblique
intersect at 90°
do not intersect
intersect NOT at 90°

5. Identify Pairs of Lines and Angles Postulates:
Section 3.1
Identify Pairs of Lines and Angles
Postulates:
Postulate 13: Parallel Postulate
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 parallel to the given line.
There is exactly one line through
P parallel to l.
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.
There is exactly one line through
P perpendicular to l.

6. EXAMPLE 2
Identify parallel and perpendicular lines
Use the markings in the diagram.
Name a pair of parallel lines. a.
MK LS
Name a pair of perpendicular lines. b.
NP PQ
Is PR LS ? Explain. c.
No, no parallel markings on PR

7. parallel GUIDED PRACTICE for Examples 1 and 2
1. Lines in the same plane that do not intersect are called________________.
2. Lines not in the same plane that do not intersect are called________________.
parallel
skew

8. Section 3.1
Identify Pairs of Lines and Angles
ANGLES AND TRANVERSALS A _____________ is a _______ that intersects two or more coplanar lines at different __________. Transversals form special angle _________.
Name the transversals in each diagram.
transversal
line
points
pairs
line a
line t
line b

9. Section 3.1
Identify Pairs of Lines and Angles
Key Concepts: Angles formed by transversals
Corresponding angles:
Two angles that have corresponding positions on the same side of a transversal.

10. Section 3.1
Identify Pairs of Lines and Angles
Key Concepts: Angles formed by transversals
Consecutive interior angles:
Two angles that lie between the two lines on the same side of a transversal.

11. Section 3.1
Identify Pairs of Lines and Angles
Key Concepts: Angles formed by transversals
Alternate interior angles:
Two angles that lie between the two lines on opposite sides of a transversal.

12. Section 3.1
Identify Pairs of Lines and Angles
Key Concepts: Angles formed by transversals
Alternate exterior angles:
Two angles that lie outside the two lines on opposite sides of a transversal.

13. Identify angle relationships
EXAMPLE 3
Identify angle relationships
Identify all pairs of angles of the given type.
Transversal connects angle pairs a.
Corresponding
Same side transversal, corresponding spots
1, 5
2, 6
3, 7
4, 8 b.
Alternate interior
Alternate sides, between two lines
2, 7
4, 5 c.
Alternate exterior
Consecutive interior d.
Alternate sides, outside two lines
Same side, between two lines
1, 8
3, 6
2, 5
4, 7

14. GUIDED PRACTICE
for Example 3
Classify the pair of numbered angles. 3.
Corresponding (CORR)

15. GUIDED PRACTICE
for Example 3
Classify the pair of numbered angles. 4.
Alternate Exterior (AE)

16. GUIDED PRACTICE
for Example 3
Classify the pair of numbered angles. 5.
Alternate Interior (AI)

17. HOMEWORK
Worksheet 3.1
Worksheet 3.1
Skip #’s 25 to 30