Download ch 03 geometry parallel lines

Some terms…
• Parallel lines
• Skew lines
• Parallel planes
Transversal and types of
angles
• Transversal
• Corresponding angles
• Alternate exterior
angles
• Alternate interior
angles
• Consecutive interior
angles (same side
1
3
2
4
5
6
7
8
Parallel and perpendicular
• Parallel Postulate
• Perpendicular Postulate
• Theorem: If two lines intersect to form a linear
pair of congruent angles, then the lines are
perpendicular
• Theorem: If two sides of two adjacent acute
angles are perpendicular, then the angles are
complementary
• Theorem: If two lines are perpendicular, then they
intersect to form four right angles
angle pairs you already
know
• What angle pairs do you
already know?
1
3
 Linear Pairs (measures are
supplementary)
• Translated into a
formula
5
7
2
4
6
8
m 1 + m 2 = 180
 Vertical Angles (measures are
congruent)
• Translated into a
Linear Pairs and Vertical Angles do not give you parallel lines!
formula
Parallel lines and angle
pairs
Corresponding Angles Postulate ()
 Translated into a formula
m 1 = m 5
m 3 = m
7
m 8 = m 4
m6 = m 2
1
Alternate Exterior Angle Theorem ()
 Translated into a formula
m 1 = m 8
m 2 = m
7
Alternate Interior Angles Postulate ()
 Translated into a formula
m 4 = m 5
m 3 = m 6
Consecutive Interior Angles Theorem (180)
 Translated into a formula
m 3 + m 5 = 180
m 4 + m 6 = 180
3
5
7
4
6
8
2
Parallel lines and angle
pairs
• Consecutive Angles Theorem
(180)
1
 Translated into a formula
3
m 3 + m 5 = 180
m 3 + m 5 = 180
5
7
4
6
8
2
Examples from Class Work
Linear Pairs (180)
Vertical Angles ()
Corresponding Angles Postulate ()
Alternate Exterior Angle Theorem ()
Alternate Interior Angle Theorem ()
83 +
Consecutive Interior Angles Theorem (180)
-83
180
3.
3
1
83
x
(y – 13 )
83 = y – 13
+13
+13
96 = y
What are
these angles
to each
x =other?
-83
x =
97
What are
these angles
to each
other?
Slope and parallel lines
• What conclusion can
you draw about
slopes of parallel
lines?
• What part of y = mx
+ b would be the
same?
• What would be
different?
Slope and Perpendicular
lines
• What conclusion can
you draw about
slopes of
perpendicular lines?
• What part of y = mx
+ b would be the
same?
• What would be
different?