Download 3.2 Parallel Lines and Transversals October 20, 2015

October 20, 2015
3.2 Parallel Lines and Transversals
Geometry
3.2 Parallel Lines and Transversals.
Essential Question
When two parallel lines are cut by a
transversal, which of the resulting pairs of
angles are congruent or supplementary?
October 20, 2015
3.2 Parallel Lines and Transversals
Theorem 3.1:Corresponding Angles
m
m || n
n
If two parallel lines are cut by a transversal, then the
pairs of corresponding angles are congruent.
October 20, 2015
3.2 Parallel Lines and Transversals
This means ALL corresponding
angles are congruent.
1
4
3
5
8
2
6
7
1  5
2  6
3  7
4  8
October 20, 2015
3.2 Parallel Lines and Transversals
Example 1
Find all angle measures in the picture.
120°
?
60°
60°
? 120°
?
120°
? ?60°
60°
? ?120°
October 20, 2015
Notice…
When two parallel lines are
cut by a transversal, any pair
of angles will either be
congruent
____________________
or
supplementary
_____________________.
3.2 Parallel Lines and Transversals
Theorem 3.2
If two parallel lines are cut by a
transversal, then alternate interior angles
are congruent.
2 lines ||  alt int s 
October 20, 2015
3.2 Parallel Lines and Transversals
Theorem 3.3
If two parallel lines are cut by a
transversal, then alternate exterior angles
are congruent.
2 lines ||  alt ext s 
October 20, 2015
3.2 Parallel Lines and Transversals
Theorem 3.4
If two parallel lines are cut by a
transversal, then the pairs of same side
interior angles are supplementary.
m1 + m2 = 180
m3 + m4 = 180
1
2
3
4
2 lines ||  ss int s supp
October 20, 2015
3.2 Parallel Lines and Transversals
Theorems in a nutshell.
2 lines ||  corr s 
October 20, 2015
3.2 Parallel Lines and Transversals
Theorems in a nutshell.
2 lines ||  alt. int. s 
October 20, 2015
3.2 Parallel Lines and Transversals
Theorems in a nutshell.
2 lines ||  alt. ext. s 
October 20, 2015
3.2 Parallel Lines and Transversals
Theorems in a nutshell.
2 lines ||  ss int. s supp.
October 20, 2015
3.2 Parallel Lines and Transversals
These are the “reasons” for proof.
2 lines || 
corr s 
alt int s 
alt ext s 
ss int s supp
October 20, 2015
3.2 Parallel Lines and Transversals
Example 2
State the theorem that justifies the
statement below.

3  6
Alt Int s

4  5
Alt Ext s

1  4
Corr. s

m6 + m7 = 180° Same Side Int s
October 20, 2015
3.2 Parallel Lines and Transversals
Example 3
Solve each problem for x and y. Identify
the theorem that justifies your answer.
a.
b.
x°
70°
y°
y°
x°
120°
October 20, 2015
3.2 Parallel Lines and Transversals
Example 4
m || n Solve for x.
(120 – x)°
5x°
m
n
2 lines ||  alt ext s 
5x = 120 – x
6x = 120
October 20, 2015
x = 20
3.2 Parallel Lines and Transversals
Example 5
(x + 20)°
(x + 8)°
m m || n Solve for x.
n
2 lines ||  SS int s supp
(x + 20) + (x + 8) = 180
2x + 28 = 180
2x = 152
x = 76
October 20, 2015
3.2 Parallel Lines and Transversals
Example 6
m || n Solve for x.
(x + 40)°
(x + 40)° (x + 50)°
m
n
Linear Pair Post.
(x + 40) + (x + 50) = 180
2x + 90 = 180
2 lines ||  corr s 
October 20, 2015
2x = 90
x = 45
3.2 Parallel Lines and Transversals
Example 7
Solve for x and y.
5x = 35
October 20, 2015
3.2 Parallel Lines and Transversals
Your Turn
In each of the following problems solve for
x and y.
a.
b.
(2x - 10)°
y°
80°
October 20, 2015
x°
100°
3.2 Parallel Lines and Transversals
Your Turn
In each of the following problems solve for
x and y.
c.
d.
130° x°
120°
3x°
y°
October 20, 2015
3.2 Parallel Lines and Transversals
Your Turn
In each of the following problems solve for
x and y.
e.
October 20, 2015
3.2 Parallel Lines and Transversals
In Summary.
2 lines || 
corr s 
alt int s 
alt ext s 
ss int s supp
October 20, 2015
3.2 Parallel Lines and Transversals
Extra for Experts
Find x. (Hint: Draw a line through the vertex of angle
x and parallel to the other two lines.)
25°
x°
43°
October 20, 2015
m
m || n
n
3.2 Parallel Lines and Transversals
Solution
25°
25°x°
43° 43°
m
m || n
n
Find x.
x° = 25° + 43° = 68°
October 20, 2015
3.2 Parallel Lines and Transversals
Parallel or not?
October 20, 2015
3.2 Parallel Lines and Transversals
Assignment
October 20, 2015
3.2 Parallel Lines and Transversals