Download 3-1 Parallel Lines and Transversals

Advanced Geometry
Parallel and Perpendicular Lines
Lesson 1
Parallel Lines
Lines (segments & rays, also)
are either parallel,
l m
intersecting,
or skew.
Skew Lines
do not intersect
are not coplanar
AB and CD
are skew.
Planes can
be parallel
OR
intersecting.
Example:
Name all segments that
are parallel toAF .
DE , BG, CH
Name all segments that
intersectGH .
BG, FG, CH , EH
Name all segments that
are skew to FG .
AD, DE , BC , CH , and CE
Name all planes that are
parallel to plane DEF.
Figure from p. 143.
Transversal
Identify the pairs of lines to which each
given line is a transversal.
m
l and n; l and p;
n and p
p
l and m; l and n;
m and n
Whenever there are two lines and a transversal,
eight angles are formed.
t
a
b
interior angles –
angles between
the two lines
∠3, ∠4, ∠5, ∠6
exterior angles –
angles outside
the two lines
∠1, ∠2, ∠7, ∠8
Alternate
Interior Angles
AIA
∠3 and ∠6
∠4 and ∠5
•both angles are interior
t
•different sides of the
transversal
Alternate
Exterior Angles AEA
a
b
•both angles are exterior
•different sides of the
transversal
∠1 and ∠8
∠2 and ∠7
Consecutive
Interior Angles
CIA
∠3 and ∠5
∠4 and ∠6
•both angles are interior
t
•same side of the
transversal
Corresponding
Angles
• one interior angle and
one exterior angle
•same side of the
transversal
a
b
∠1 and ∠5
∠2 and ∠6
∠3 and ∠7
∠4 and ∠8
Identify each pair of angles and AIA, AEA, CIA,
corresponding angles, vertical angles, or a linear pair.
∠5 and ∠12
AEA
∠10 and ∠3
corresponding angles
∠4 and ∠7
vertical angles
∠10 and ∠11
CIA
∠2 and ∠12
linear pair
∠3 and ∠14
AIA
Name the transversal that forms each pair of angles.
Then identify the pair of angles.
∠8 and ∠6
a
corresponding angles
∠10 and ∠14
b
AIA
∠2 and ∠16
c
AEA
∠10 and ∠11
b
CIA
When the lines cut by a transversal are parallel,
the four angle pairs have a special relationship.
• AIA are congruent.
Reminder:
• AEA are congruent.
• CIA are supplementary.
• Vertical angles
are ALWAYS
congruent.
• Corresponding angles
are congruent.
• Linear pairs are
ALWAYS
supplementary.
In the figure a || b and m∠4 = 51. Find the measures
of all numbered angles. Justify each answer.
a
b
Find the measure of each angle if m∠1 = 62
and m∠7 = 107.
What is the measure of ∠RTV?
If m∠2 = 4x + 7 and m∠3 = 5x – 13, find m∠3.
If m∠5 = 2x – 10, m∠6 = 4(y – 25),
and m∠7 = x + 15. find x and y.