section 3-1 definitions: parallel lines and angles
DESCRIPTION
SECTION 3-1 DEFINITIONS: PARALLEL LINES AND ANGLES. Parallel Lines. Definition – Coplanar lines that do not intersect. l. Symbol: || Notation: Line l || line m. A. B. C. D. m. Segments and Rays contained in parallel lines are also parallel. A. B. C. D. AB || CD. AB || CD. - PowerPoint PPT PresentationTRANSCRIPT
Definition – Coplanar lines that do not intersect
Symbol: ||
Notation:
Line l || line m
BAl
C D
m
Segments and Rays contained in parallel lines are also
parallel.BA
C D
AB || CD AB || CD
In the diagram, PQ and RS do not intersect.
Since they are parts of lines,
they will eventually intersect.
P
Q
R S
But they are NOT parallel.
Definition - Non-coplanar lines that do not intersect
H
F
D
B C
A
E
G
AE and CG are not skew, they are parallel.
Why??
Plane AEGC can be created, so AE and CG are
considered coplanar lines
that never intersect.
H
F
D
C
G
EA
B
Definition – planes that do not intersect
Plane AEHD || Plane CFGB
Theorem 3-1: If two parallel planes (A and B) are cut by a third plane
(C), then the lines of intersection are parallel.
A
B
C l
m
Plane B Plane C
Plane A Plane C
line l
line m
Therefore, line l || line m
A line that intersects two or more coplanar lines in different points.
a
m
b
lt
t
a
b
t
1 2
3 4
5 6
7 8
Definition: Two nonadjacent interior angles on opposite sides of the transversal.
Alternate Interior Angles
Alternate Exterior Angles
3 & 6
4 & 5
1 & 8 2 & 7
a b
t1
2
3 4
5 67
8
Same-Side Interior Angles
Same-Side Exterior Angles
3 & 4
5 & 6
1 & 8
2 & 7
Definition: Two interior angles on the same side of the transversal.
a
b
t
1 2
3 4
5 6
7 8
1 & 5
2 & 6
3 & 7
4 & 8
Definition: Two angles in corresponding positions relative to the two lines.
a
b
t
1 5
2 6
3 7
4 8
1) 1 & 3
2) 3 & 6
3) 8 & 5
4) 2 & 1
5) 1 & 8
6) 2 & 4
7) 5 & 3
8) 3 & 7
9) 6 & 7
10) 2 & 5
11) 2 & 3
12) 4 & 5
Identify the types of angles.
Corresponding s
Corresponding s
Alternate Interior s
Same-Side Interior
NO RELATIONSHIP
Alternate Exterior s
Same-Side Interior
Alternate Exterior
Linear Pair
Same-Side Exterior s
Linear Pair Vertical Angles
1 52 6
3 74 8
1314
1516
910
1112
Identify the types of angles.
13) 4 & 12 17) 15 & 16
14) 6 & 11 18) 1 & 14
15) 5 & 10 19) 7 & 11
16) 10 & 13 20) 3 & 15
Corresponding s
Alternate Exterior AnglesNo Relationship
Same-Side Interior s
Linear Pair
Vertical Angles
Alternate Interior s
Same-Side Exterior s