Download same side

Warm-Up

Use the diagram below


Name a pair of complementary angles
Name a pair of supplementary angles
5
4
3
2
1
Properties of Parallel Lines

Transversal

A line that intersects two other lines at two
distinct points
Interior VS. Exterior
What does interior mean?
The space between the two parallel lines.
What does exterior mean?
The space not between the two parallel
lines.
EXTERIOR
INTERIOR
EXTERIOR
Alternate VS. Same Side
What does alternate mean?
On different sides of the transversal.
What does same side mean? On the same side of the transversal.
Angles formed by a transversal

Alternate Interior Angles

1 and 2 are alternate interior angles
1
1
2
1
2
1
2
2
Parallel Lines

Alternate Interior Angles

On parallel lines, alternate interior angles are
congruent.
1
3
<1 = <2
<3 = <4
4
2
Angles formed by a transversal

Alternate Exterior Angles

1 and 2 are alternate exterior angles
1
1
2
2
1
1
2
2
Parallel Lines

Alternate Exterior Angles

On parallel lines, alternate exterior angles are
congruent.
1
3
<1 = <2
<3 = <4
4
2
Angles formed by a transversal

Same Side Interior Angles

1 and 2 are same side interior angles
1
1
2
1
2
2
1
2
Parallel Lines

Same Side Interior Angles

On parallel lines, same side interior angles are
supplementary
1
3
<2 + <3 = 180°
<1 + <4 = 180°
4
2
Angles formed by a transversal

Same Side Exterior Angles

1 and 2 are same side exterior angles
1
1
2
2
1
1
2
2
Parallel Lines

Same Side Exterior Angles

On parallel lines, same side exterior angles are
supplementary
1
3
<2 + <3 = 180°
<1 + <4 = 180°
4
2
Angles formed by a transversal

Corresponding Angles


One angle in the interior and one in the exterior.
Corresponding angles are also on the same side of the
transversal.
6
5
1
3
2
4
7
8
Angles formed by a transversal

Corresponding Angles

1 and 2 are same side exterior angles
1
1
2
2
1
2
1
2
Parallel Lines

Corresponding Angles

On parallel lines, corresponding angles are
congruent.
5 6
1 3
<1
<2
<3
<4
2
4
7
8
=
=
=
=
<7
<6
<8
<5
Let’s Identify Some Angles
What kind of angles are <1 & <2?
1.
2.
2
5.
1
1
2
1
2
2
1
1
6.
4.
3.
7.
2
2
1
2
1
1.
2.
3.
4.
alt. exterior
alt. interior
corresponding
same side
interior
5. same side
exterior
6. no relation
7. corresponding
Let’s Identify Some Angles
Identify each pair of angles.
same side exterior
1. < 1 & < 2 _________________
1
2
3
vertical
2. < 2 & < 3 _________________
3. < 3 & < 4 _________________
alternate interior
4. < 4 & < 5 _________________
supplementary
8
7 6
5 4
5. < 5 & < 6 _________________
alternate interior
6. < 4 & < 7 _________________
alternate exterior
7. < 3 & < 5 _________________
same side interior
8. < 5 & < 8 _________________
corresponding
Parallel Lines

All of the angles that we have discussed
have special qualities when they are
formed by parallel lines.
This is the symbol that lets us know that lines are
parallel to each other.
Finding The Measures of Angles
Find the value of <1 & <2.
1.
2.
1
103°
111°
1
2
2
1
5.
52°
2
1
47°
97°
42°
1
2
4.
3.
2
43°
1. <1=103
<2=103
2. <1=42
<2=138
3. <1=103
<2=97
4. <1=69
<2=133
5. <1=43
<2=52
Using Algebra With Parallel Lines
3.
Solve for x.
1.
2.
7x-9
22x+17
5x+16
8x+13
7x+20
4x+21
4.
15x-11
9x+25
1.
2.
3.
4.
x=10
x=5
x=12
x=6