Download MJ2A - Davidsen Middle School

MJ3
Ch 6.1 – Line & Angle Relationships
1. In art class Mark mixed 3 liters of yellow paint, 2 liters
of red paint and 1 liter of blue paint. How many milliliters
of paint did Mark mix in the bucket?
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3  2  1  6 liters
(1 liter = 1000 milliliters)
6 liters = 6000 milliliters
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Assignment Review
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None
Before we begin….
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Please take out your notebook and get ready
to work…
Today we will look at angles from a different
perspective…That is angles formed by 2
parallel lines cut by a transversal….
Before we do that we need to make sure
everyone understands the vocabulary used
when talking about lines and angle
relationships…
Objective
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Students will identify line and angle
relationships
Vocabulary
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Acute Angles – have a
measure less than 90°
Right Angles – have a
measure equal to 90°
Obtuse Angles – have a
measure greater than
90°
Straight Angles – have
a measure of 180°
Vocabulary
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Parallel lines – Two lines on a plane that
never intersect.
Transversal – A line that intersects 2 parallel
lines and creates 8 angles.
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Interior angles lie inside the parallel lines
Exterior angles lie outside the parallel lines
Alternate interior angles are on opposite sides of
the transversal and inside the parallel lines
Alternate exterior angles are on opposite sides of
the transversal and outside the parallel lines.
Corresponding angles are in the same position on
the parallel lines in relation to the transversal
Properties
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If two parallel lines are cut by a transversal,
then the following pairs of angles are
congruent.
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Corresponding angles are congruent
Alternate interior angles are congruent
Alternate exterior angles are congruent
Let’s look at an example…
Parallel Lines Cut by a Transversal
a
c
e
g
 a = 110°
f
h
b
d
Your Turn
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In the notes section of your notebook draw
two parallel lines cut by a transversal. Then
find an acute angle and give it the measure of
60°. Then find the measure of the remaining
angles.
More Lines & Angle
Relationships
Intersecting Lines and Angles
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Vertical Angles – Angles formed by two
intersecting lines. Vertical angles are
congruent
Example
4
1
3
2
Angles 1 & 3 are vertical angles
Angles 2 & 4 are vertical angles
Adjacent Angles
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When two angles have the same vertex,
share a common side, and do not overlap
they are adjacent angles
Example
Angle 1 & 2 are adjacent angles
The mAOB = m1 + m2
A
1
2
O
B
Complimentary Angles
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If the sum of the measures of two angles
equal 90°, the angles are complimentary
Example:
3
4
1
2
You may see complimentary angles displayed 2 ways as pictured above.
If the measures of the angles equal 90°, then they are complimentary
Supplementary Angles
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If the sum of two angles equals 180°, then
the angles are supplementary
Example
1
2
3
4
You may see supplementary angles displayed 2 ways as pictured above.
If the measures of the angles equal 180°, then they are supplementary
Finding the Missing Measure
You can find the missing measure of a pair of
angles by classifying the angles then subtract
the given measurement from the total
measurement.
Example:
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You can find the value of x by classifying
the angles as supplementary and = 180°
Then subtract 118° from 180°
118°
to get the value of x = 62°
x°
Summary
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In the notes section of your notebook
summarize the key concepts covered in
today’s lesson
Today we discussed…
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Parallel lines cut by a transversal
Vertical angles
Complimentary angles
Supplementary angles
Assignment
Practice skills workbook Lesson 6.1
Reminder
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This assignment is due tomorrow.
I do not accept late assignments