Download Properties of Parallel Lines

Geometry CP2 (Holt 3-2)
K.Santos
Parallel Lines
1
5 6
2
3
7 8
4
Postulate and Theorems
If two lines are parallel, then …
Corresponding Angles Are Congruent:
<1≅<3
<2 ≅ <4
<5 ≅ <7
Alternate Interior Angles Are Congruent:
<2 ≅ <7
<3 ≅ <6
Alternate Exterior Angles are Congruent:
<1 ≅ <8
<4 ≅ <5
<6 ≅ <8
More Theorems
Same-Side Interior Angles are Supplementary:
<2 and <3 are supplementary
<6 and <7 are supplementary
Same-Side Exterior Angles are Supplementary:
<1 and < 4 are supplementary
<5 and <8 are supplementary
Overview
110 70
70 110
110 70
70 110
F
U
N
True only if the lines are parallel
corresponding angles
same-side interior angles
alternate interior angle
Angles are either congruent or supplementary
Fill in the missing angles
Lines a and b are parallel.
a
130°
There are congruent vertical angles
There are linear pairs that are supplementary
There are congruent corresponding angles
And there are many other congruent and supplementary angles
b
Finding measures of angles
In the diagram at the right, a || b. Find m< 1 and m <2.
t
< 1 and 42° corresponding angles (≅)
42°
a
So m < 1 = 42°
2
<1 & <2 are supplementary
m<1 + m<2 = 180°
42 + m< 2= 180
m< 2 = 138°
1
b
Finding angle measures
Find m<ECF and m<DCE
A
D
B 4x+22°
70°
G
<ECF ≅ <GCB (corresponding angles)
m<ECF = 70°
<ABC ≅ <DCE (corresponding angles)
4x + 22= 5x
22= x
m<DCE = 5x
m<DCE = 5(22)= 110°
There are other equations that you could have used
5x°
C
F