Download Lesson 11: Very Short version Lesson 12: Angles Associated with

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Transcript 
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Lesson 11: Very Short
version
8th grade, module 2. A wrap up of
transformations and new definition of
congruency
Lesson 12: Angles
Associated with Parallel
Lines
+
Congruent
n 
What did we decide stayed congruent in our
transformations?
+
New Definition for Congruence:
A sequence of of basic rigid motions that
maps one figure onto another.
Figures are equal in all ways other than their location; they
are congruent
≅
+
Congruence
A’
A
?
A’
≅
A
+
Congruency and angles
Transversal:
A line that passes
through two lines
+
L1 & L2 are not parallel
m is a transversal
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L1 & L2 ARE parallel
m is a transversal
Informal arguments that support claims of equality:
What do we know about transformations that can
support
rules of equality and angles on parallel lines with a
transversal?
+
Vertical angles:
Opposite angles made by two intersecting lines
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Corresponding angles:
Matching corners; same relative position at intersections
3
3
7
8
4
4
+
Alternate interior angles:
Two interior angles that lie on different lines and on opposite
sides of a transversal
3
3
7
8
4
4
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Same side interior angles:
Same side of the transversal in inside the two lines.
3
3
4
4
+
Alternate exterior angles:
The pairs of angles on opposite sides of a
transversal on the exterior of the lines
7
7
8
8
+
Same side exterior angles:
Pair of angles on the same side of the transversal
outside the lines.
+
Angle relationships in summary
n 
Equal angles
n  Vertical angles
n 
Supplementary angles
n  Same side interior angles
n 
Corresponding angles
n 
Same side exterior angles
n 
Alternate interior angles
n 
Adjacent angles
n 
Alternate exterior angles
+
Review
n 
What are the different types of
angle pairs’ names?
n 
Which are equal?
n 
Which are supplementary?
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Which angles are equal to A?
Green lines are parallel
A B
C D
E F
G H
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Which angles are equal to B?
Green lines are parallel
A
B
C D
E
G
F
H
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Find the missing angles:
G = 113º
Green lines are parallel
A B
C D
E F
G H
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Find the missing angles:
F = 67º
Green lines are parallel
A B
C D
E F
G H
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Find the missing angles:
A = 49º
Green lines are parallel
A
B
C D
E
G
F
H
+
Find the missing angles:
D = 73º
Green lines are parallel
A B
C D
E F
G H
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Solve for the angles
+
Solve for the angles
2x + 4
3x + 1
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