Download Alternate Interior Angles two nonadjacent interior angles on

Section 2.2 ­ Exploring Parallel Lines
Let's look at other types of angles formed when a transversal intesects parallel lines.
Alternate Interior Angles two non­adjacent interior angles on opposite sides of a transversal
AIA AIA
AIA AIA
If we made the lines parallel, what conjecture could be made
about the alternate interior angles?
When a transversal intersects two parallel lines, the alternate interior angles are equal.
Is the converse of this statement true?
If a transversal intersects two lines such that the alternate interior angles are equal, then the lines are parallel
1
Opposite Angles two non­adjacent angles formed when two straight lines intersect
Can you make a conjecture
about the measurement of
opposite angles?
OA OA
OA OA
Opposite angles are equal.
2
Alternate Exterior Angles two exterior angles between two lines and a transversal, on opposite sides of the transversal
AEA AEA
AEA
AEA
If we made the lines parallel, what conjecture could be made
about the alternate exterior angles?
When a transversal intersects two parallel lines, the alternate exterior angles are equal.
Is the converse of this statement true?
If a transversal intersects two lines such that the alternate exterior angles are equal, then the lines are parallel
3
Co­interior Angles two interior angles between two lines on the same side of the transversal
CIA CIA
CIA CIA
If we made the lines parallel, what conjecture could be made
about the co-interior angles?
When a transversal intersects two parallel lines, the co­interior angles are supplementary.
Is the converse of this statement true?
If a transversal intersects two lines such that the co­interior angles are supplementary, then the lines are parallel
4
Naming Angles
D
This angle can be named
<
<ABD or DBA.
Sometimes we name angles
by numbers rather than the
capital letters of the lines.
3
A
C
B
E
Sometimes we name angles
by lower case letters rather
than the capital letters of
the lines.
a
b
c
d
e f
5
# 2
Exercises: Page 72
Draw the diagram in the book like this; so numbers are used for the angles.
Create a table like below to write your answers. I've done an example for you.
Angles That Are Equal <
1 = <4 1
2
3
4
5
6
7
8
Types of Angles Opposite Angles 6
Ex(1) Find all the indicated angles in the diagram below. Justify your choices.
b
c
a
d e f
g h
k
i j
m
7
Ex(2)
Based on the given information, prove that the lines m and n are parallel. 133o
m
a b
47o c
n
TWO COLUMN PROOF
Statement Justification
Exercises: Pages 78 ­ 82 #
1 ­ 4
8
When a transversal intersects two parallel lines, the alternate interior angles are equal.
Let's prove this statement deductively.
Ex(1) A transversal intersects a pair of parallel lines. Prove deductively that the alternate interior angles < 3 and < 2 are equal. 1
3
4
5
2
TWO COLUMN PROOF
Statement Justification
9
When a transveral intersects two parallel lines, the co­interior angles are supplementary.
Let's prove this statement deductively.
Ex(2) Use a two­column proof to deductively prove that < 3 and < 4 are supplementary in the problem below.
8
7
1
3
4
2
TWO COLUMN PROOF
Statement Justification
m
6
5
n
p
10
11