Download Geometry 3-1: Lines and Angles Parallel lines are coplanar lines

Geometry
3-1: Lines and Angles
Parallel lines are coplanar lines that do not intersect.
Examples: EG and AC; GH and EF
F
H
E
G
Skew lines are non-coplanar lines that do not intersect.
Examples: EF and GC; AC and HD
D
B
Perpendicular lines intersect at right angles.
Examples: AB and AC; GH and HD
C
A
Parallel planes are planes that do not intersect.
Examples: Plane EGH and plane ABC; plane ABE and plane CDG
Ex. 1: Use the sketch to name the following.
a) Two parallel lines: BE and CF; AC and DF or others
b) Two perpendicular lines: CF and EF
c) Two skew lines: BE and CA; EF and AB or others
d) Two parallel planes: plane ABC and plane DEF
Special Angle Pairs
A transversal is a line that intersects two
coplanar lines.
Ex: line t
Corresponding angles are two angles on the
same side of the transversal and the same side of
the intersected lines. (They’re basically in the
same position.)
Ex: ∠1 and ∠5, ∠2 and ∠6, etc.
Alternate interior angles are two non-adjacent
angles on opposite sides of the transversal and in
between the intersected lines.
Ex: ∠3 and ∠6, ∠4 and ∠5
t
1
2
3
n
4
5
7
6
m
8
Alternate exterior angles are two non-adjacent angles on opposite sides of the transversal and
outside the intersected lines. Ex: ∠1 and ∠8, ∠2 and ∠7
Same-side interior angles are two angles on the same side of the transversal in between the
intersected lines. Ex: ∠3 and ∠5, ∠4 and ∠6
Ex. 2: Use the figure to name the following:
a) The transversal: line b
b) A pair of corresponding angles: ∠1 and ∠5, ∠3 and ∠6, etc.
c) A pair of alt. int. angles: ∠4 and ∠6, ∠2 and ∠5
d) A pair of alt. ext. angles: ∠1 and ∠8, ∠3 and ∠7
e) A pair of same-side int. angles: ∠4 and ∠5, ∠2 and ∠6
Ex. 3: For each pair, list the transversal and the type of angles:
a) ∠4 and ∠10: y, same-side interior
b) ∠2 and ∠5: z, alternate interior
c) ∠11 and ∠8: x, corresponding
c
a
1
3
4
2
5
7
6
8
9 11
10 9
9
7
z
5
1 4
6
8
3
2
x
y
Ex. 4: Use the figure from Ex. 3.
a) Name a pair of alt. ext. angles along transversal z: ∠1 and ∠8, ∠3 and ∠7
b) Name a pair of corresponding ∠s along transversal y: ∠3 and ∠9, ∠2 and ∠10, ∠4 and ∠11
c) Name a pair of same-side int. angles along transversal x: ∠11 and ∠7, ∠5 and ∠10
b