parallel lines advanced geometry parallel and perpendicular lines lesson 1
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Parallel Lines
Advanced GeometryParallel and Perpendicular Lines
Lesson 1
Lines (segments & rays, also) are either
intersecting,
or skew.
l m
parallel,
AB CD
and
are skew.
do not intersect
Skew Lines
are not coplanar
Planes can be parallel
OR
intersecting.
Name all segments that are parallel to .
Name all segments that are skew to .
Name all segments that intersect .
AF
GH
FG
Example:
Name all planes that are parallel to plane DEF.
, ,DE BG CH
, , ,BG FG CH EH
, , , ,AD DE BC CH and CE
Figure from p. 143.
TransversalIdentify the pairs of lines to which each
given line is a transversal.
m
p
l and n; l and p; n and p
l and m; l and n; m and n
Whenever there are two lines and a transversal, eight angles are formed.
interior angles – angles between the two lines
exterior angles – angles outside the two lines
∠3, ∠4, ∠5, ∠6 ∠1, ∠2, ∠7, ∠8
a
b
t
Alternate Interior Angles
•different sides of the transversal
AIA
•both angles are interior
•different sides of the transversal
AlternateExterior Angles AEA
•both angles are exterior
∠3 and ∠6∠4 and ∠5
∠1 and ∠8∠2 and ∠7
a
b
t
Alternate Interior Angles
Alternate Interior Angles
AlternateExterior AnglesAlternateExterior Angles
Consecutive Interior Angles
•same side of the transversal
CIA
•both angles are interior
•same side of the transversal
Corresponding Angles
•one interior angle and one exterior angle
∠3 and ∠5∠4 and ∠6
∠1 and ∠5∠2 and ∠6∠3 and ∠7∠4 and ∠8
a
b
t
Consecutive Interior Angles
Consecutive Interior Angles
Identify each pair of angles and AIA, AEA, CIA, corresponding angles, vertical angles, or a linear pair.
∠5 and ∠12
∠10 and ∠3
∠4 and ∠7
∠10 and ∠11
∠2 and ∠12
∠3 and ∠14
AEA
corresponding angles
vertical angles
CIA
linear pair
AIA
Name the transversal that forms each pair of angles. Then identify the pair of angles.
∠8 and ∠6
∠10 and ∠14
∠2 and ∠16
∠10 and ∠11
corresponding angles
AIA
AEA
CIA
a
b
c
b
When the lines cut by a transversal are parallel,the four angle pairs have a special relationship.
•AIA are congruent.
•AEA are congruent.
•CIA are supplementary.
•Corresponding angles are congruent.
Reminder:•Vertical angles are ALWAYScongruent.•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.∠