072 Parallel and Perpendicular Lines.notebook December 17, 2013
072 Parallel and Perpendicular Lines.notebook December 17, 2013
a
34
1 2b
intersecting lines - lines that cross
vertical angles - diagonal from each other on same line
congruent angles - have same measurement
supplementary - sum of 180 (straight line)
complementary - sum of 90
a & b
2 & 4, 1 & 3 Congruent
2 & 4, 1 & 3
1 & 2, 2 & 3, 3 & 4, 1 & 4
Use the figure to identify the following terms.
072 Parallel and Perpendicular Lines.notebook December 17, 2013
MathBook pg 330
OH Academic Content Standards8.3.2
(pp 7)
Students will learn to identify parallel and perpendicular lines and the angles formed by a transversal and will show understanding through class work and quiz.
Learning Objective
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Parallel lines are lines in a plane that never meet, such as the lines that mark the lanes in a sprinting race.
072 Parallel and Perpendicular Lines.notebook December 17, 2013
When we study slope, we will be putting parallel and perpendicular lines on a coordinate grid and compare the slopes of the different lines formed.
Why do we need to learn this???????
We will just have to look at the equation to know what the lines are going to look like.
And to solve problems like this...
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Geometry and Spatial Sense Standard2. Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal.
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Parallel Lines and TransversalsWhen parallel lines are cut by a transversal, there are special relationships among the angles formed.
1 23
4567
8
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Parallel lines cut by a transversal form 8 angles:4 acute and 4 obtuse.
120o
60o 120o60o
120o
120o60o60o
The acute angles are all congruent.
The obtuse angles are all congruent.
Any acute angle is supplementary to any obtuse angle.
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Interior angles - angles inside the parallel lines 1, 2, 3, 4
Exterior angles - angles outside the parallel lines 5, 6, 7, 8
67
5
4
1
2
n
3
8
m
t
072 Parallel and Perpendicular Lines.notebook December 17, 2013
1 23
4
56
7
8
Alternate interior anglesare between the two lines and are on opposite sides of the transversal. (are congruent)
Alternate exterior anglesare outside of the two lines and are on opposite sides of the transversal. (are congruent)
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Corresponding anglesare in the same position with respect to the transversal. (are congruent)
1 238
4
56
7
Corresponding angles are congruent IF the lines are parallel.
1 & 7, 2 & 5, 8 & 6, 3 & 5
http://www.youtube.com/watch?v=iMINKDZkuM
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Some pairs of the eight angles formed by two parallel lines and a transversal have special names.
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Angles 6 and 7 are alternate exterior angles. Define this term and list another pair of them.
Angles 1 and 4 are alternate interior angles.Define this term and list another pair of them.
6 7
5
4
1
2
n
3
8
m
t
inside the parallel lines and on opposite sides of the transversal 2 & 3
outside the parallel lines and on opposite sides of the transversal 5 & 8
(pp 8)
072 Parallel and Perpendicular Lines.notebook December 17, 2013
6 7
5
4
1
2
n
3
8
m
t
Vertical angles
Corresponding angles - angles in the same spot but on a different line
5 & 2, 1 & 6, 3 & 8, 4 & 7
5 & 3, 1 & 7, 6 & 4, 2 & 8
**Corresponding angles are congruent if the lines are parallel.
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Students will learn to identify parallel and perpendicular lines and the angles formed by a transversal and will show understanding through class work and on quiz.
Learning Objective
How are we doing?http://www.youtube.com/watch?v=2lcn0pmVniA
072 Parallel and Perpendicular Lines.notebook December 17, 2013
n
7
1
4
8
2
3
56
t
p
Lines n and p are parallel.
Name all pairs of each angle.
Vertical
Alternate Interior
Alternate Exterior
Corresponding
072 Parallel and Perpendicular Lines.notebook December 17, 2013
n
7
1
4
8
2
3
56
t
p
m 1 is 60 .
Find m 8, m 5, m 4.
458
072 Parallel and Perpendicular Lines.notebook December 17, 2013
8 7
4
6
1
5
32
p q
t
Name the vertical angles.
Name the corresponding angles.
Name the supplementary angles.m 6 = 56 .
m 5 m 2 m 8
(pp 9)
072 Parallel and Perpendicular Lines.notebook December 17, 2013
l
a
b
1 2
3 4
5 6
7 8
l
Use the diagram to identify each term.
1. Parallel lines 6. Exterior angles
2. Transversal 7. Alternate interior angles
3. Angles formed 8. Alternate exterior angles
4. Corresponding angles 9. Vertical angles
5. Interior angles 10. Supplementary angles
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Line l is parallel to line m and are intersected by transversal n. Angle b is 78°. Find the measure of the other angles.
f
g
e
d h
b
c
a
l
m
n
m am cm d
m em f
m g
m h
072 Parallel and Perpendicular Lines.notebook December 17, 2013
Students will learn to identify parallel and perpendicular lines and the angles formed by a transversal and will show understanding through class work and quiz.
Learning Objective
http://www.youtube.com/watch?v=5g0OT76xKg
Review
http://www.youtube.com/watch?v=7RiE9e037lY