Post on 02-Feb-2016
description
Learn to name, measure, classify, estimate, and draw angles.
Course 1
7-2 Angles
Vocabulary
anglevertexacute angleright angleobtuse anglestraight angle
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Course 1
7-2 Angles
Course 1
7-2 Angles
An angle is formed by two rays with a common endpoint, called the vertex. An angle can be named by its vertex or by its vertex and a point from each ray. The middle point in the name should always be the vertex.
Angles are measured in degrees. The number of degrees determines the type of angle. Use the symbol ° to show degrees: 90° means “90 degrees.”
Course 1
7-2 Angles
An acute angle measures less than 90°.
A right angle measures exactly 90°.
Course 1
7-2 Angles
An obtuse angle measures more than 90° and less than 180°.
A straight angle measures exactly 180°.
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7-2 Angles
Additional Example 1: Measuring an Angle with a Protractor
Use a protractor to measure the angle. Tell what type of angle it is.
• Place the center point of the protractor on the vertex of the angle.
G H
F
Course 1
7-2 Angles
To estimate the measure of an angle, compare it with an angle whose measure you already know. A right angle has half the measure of a straight angle. A 45° angle has half the measure of a right angle.
Lesson Quiz
Use a protractor to draw an angle with the given measure. Tell what type of angle it is.
1. 140°
2. 20°
3. Draw a right angle.
4. Is the angle shown closer to 30° or 120°?
acute
obtuse
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30°
Course 1
7-2 Angles
Learn to understand relationships of angles.
Course 1
7-3 Angle Relationships
Vocabulary
congruentvertical anglesadjacent anglescomplementary anglessupplementary angles
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Course 1
7-3 Angle Relationships
Course 1
7-3 Angle Relationships
When angles have the same measure, they are said to be congruent.
Vertical angles are formed opposite each other when two lines intersect. Vertical angles have the same measure, so they are always congruent. MRP and NRQ are vertical angles.
MRN and PRQ are vertical angles
M N160°
160°
20° 20°R
P Q
Course 1
7-3 Angle Relationships
Adjacent angles are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent.
MRN and NRQ are adjacent angles. They share vertex R and RN.
NRQ and QRP are adjacent angles. They share vertex R and RQ.
M N160°
160°
20° 20°R
P Q
Course 1
7-3 Angle Relationships
Additional Example 1A: Identifying Types of Angle Pairs
Identify the type of each angle pair shown.
A.
5 and 6 are opposite each other and are formed by two intersecting lines.
They are vertical angles.
5 6
Course 1
7-3 Angle Relationships
Additional Example 1B: Identifying Types of Angle Pairs
Identify the type of each angle pair shown.
B. 7 and 8 are side by side and have a common vertex and ray.
They are adjacent angles.
7 8
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7-3 Angle Relationships
65° + 25° = 90°
LMN and NMP are complementary.
Complementary angles are two angles whose measures have a sum of 90°.
P
N
M
L
25°65°
Course 1
7-3 Angle Relationships
Supplementary angles are two angles whose measures have a sum of 180°.
65° + 115° = 180°
GHK and KHJ are supplementary.
J
K
H
115°65°
G
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7-3 Angle Relationships
Additional Example 2A: Identifying an Unknown Angle Measure
Find each unknown angle measure.
71° + a = 90°–71° –71°
a = 19°
The sum of the measures is 90°.
a
71°
A. The angles are complementary.
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7-3 Angle Relationships
Additional Example 2B: Identifying an Unknown Angle Measure
Find each unknown angle measure.
125° + b = 180°–125° –125°
b = 55°
The sum of the measures is 180°.
b125°
B. The angles are supplementary.
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7-3 Angle Relationships
Additional Example 2C: Identifying an Unknown Angle Measure
Find each unknown angle measure.
c = 82° Vertical angles are congruent.
c 82°
C. The angles are vertical angles.
Lesson Quiz
Give the complement of each angle.
1. 70° 2. 42°
Give the supplement of each angle.
3. 120° 4. 17°
5. Identify the type of angle pair shown.
48°20°
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60° 163°
Course 1
7-3 Angle Relationships
adjacent
Learn to classify the different types of lines.
Course 1
7-4 Classifying Lines
Vocabulary
parallel linesperpendicular linesskew linesintersecting linestransversal
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Course 1
7-4 Classifying Lines
Course 2
7-3 Parallel and Perpendicular Lines
The symbol means “is parallel to.” The symbol means “is perpendicular to.”
Reading Math
Course 1
7-4 Classifying Lines
Intersecting lines are lines that cross at one common point.
Parallel lines are lines in the same plane that never intersect.
Line YZ intersects line WX.
YZ intersects WX.
Line AB is parallel to line ML.
AB ML.
YW
Z X
B
A
M
L
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7-4 Classifying Lines
Perpendicular lines intersect to form 90° angles, or right angles.
Line RS is perpendicular to line TU.
RS TU.S
R
T U
The square inside a right angle shows that the rays of the angle are perpendicular.
Writing Math
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7-4 Classifying Lines
Skew lines are lines that lie in different planes. They are neither parallel nor intersecting.
Line AB and line ML are skew.
AB and ML are skew.
M
L
AB
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7-4 Classifying Lines
Additional Example 1A: Classifying Pairs of Lines
Classify each pair of lines.
A.
The lines intersect to form right angles.
They are perpendicular.
Course 1
7-4 Classifying Lines
Additional Example 1B: Classifying Pairs of Lines
Classify each pair of lines.
B.
The lines are in different planes and are not parallel or intersecting.
They are skew.
Course 1
7-4 Classifying Lines
Additional Example 1C: Classifying Pairs of Lines
Classify each pair of lines.
C.
The lines are in the same plane. They do not appear to intersect.
They are parallel.
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7-4 Classifying Lines
Additional Example 1D: Classifying Pairs of Lines
Classify each pair of lines.
D.
The lines cross at one common point.
They are intersecting.
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7-4 Classifying Lines
Additional Example 2: Application
The handrails on an escalator are in the same plane. What type of line relationship do they represent?
The handrails are in the same plane and do not intersect.
The lines are parallel.
Course 1
7-4 Classifying Lines
Try This: Example 2
The roads are in the same plane. What type of line relationship do they represent?
The lines cross at one common point.
The lines are intersecting.
Course 2
7-3 Parallel and Perpendicular Lines
A transversal is a line that intersects two or more lines. Eight angles are formed when a transversal intersects two lines. There are 4 interior angles and 4 exterior angles. When those two lines are parallel, all of the acute angles formed are congruent, and all of the obtuse angles formed are congruent. These obtuse and acute angles are supplementary.
1 2
3 45 6
7 8