Download Lesson 1-3 - Math Slide Show

Lesson 1-3
Objective - To name, measure, and draw angles.
Exterior
A
Vertex
Point A
B
Angle Name
BAC
CAB
Interior
Sides
A

AB

AC
C
Angle - Difficult to define. Formed at the
intersection of two rays or line segments.
B
A
Types of Angles
Acute - Angles
that measure
less than 90.
Obtuse - Angles that
measure more than 90
and less than 180.
Right - Angles
that measure
exactly 90.
Straight - Angles
that measure
exactly 180.
Using a Protractor to Measure Angles
E
C
D
Name the following.
g
One Acute Angle
BEC or CEB
Two Right Angles
AED or DEA
CED or DEC
Two Obtuse Angles
AEB or BEA
BED or DEB
One Straight Angle
AEC or CEA
Using a Protractor to Measure Angles
Steps
1) Line up the protractor to the angle’s baseline.
Using a Protractor to Measure Angles
Angle Opens Right
Use Inside Numbers
Vertex in
center of hole
Steps
1) Line up the protractor to the angle’s baseline.
45
Vertex in
center of hole
Baseline
on zero degrees
Steps
1) Line up the protractor to the angle’s baseline.
2) Read the measure of the other ray.
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
1
Lesson 1-3
Using a Protractor to Measure Angles
Angle Opens Right
Use Inside Numbers
Using a Protractor to Measure Angles
Angle Opens Right
Use Inside Numbers
60
Angle Opens Left
Use Outside Numbers
Baseline
on zero degrees
Steps
1) Line up the protractor to the angle’s baseline.
Vertex in
center of hole
Steps
1) Line up the protractor to the angle’s baseline.
2) Read the measure of the other ray.
Draw a 37 angle that opens right.
Draw a 37 angle that opens right.
Steps
1) Draw baseline.
Steps
1) Draw baseline.
2) Line up
p
protractor.
3) Mark angle.
Vertex in
center of hole
Draw a 37 angle that opens right.
Baseline
on zero degrees
Draw a 152 angle that opens right.
Steps
1) Draw baseline.
Steps
1) Draw baseline.
2) Line up
p
protractor.
3) Mark angle.
4) Draw ray.
5) Label angle
measure.
37
If angle < 90 , it should
look acute.
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
2
Lesson 1-3
Draw a 152 angle that opens right.
Draw a 152 angle that opens right.
Steps
1) Draw baseline.
Steps
1) Draw baseline.
2) Line up
p
protractor.
2) Line up
pprotractor.
3) Mark angle.
3) Mark angle.
4) Draw ray.
Vertex in
center of hole
Baseline
on zero degrees
Draw a 58 angle that opens left.
Steps
1) Draw baseline.
152
If angle > 90 , it should
look obtuse.
5) Label angle
measure.
Draw a 58 angle that opens left.
Steps
1) Draw baseline.
2) Line up
pprotractor.
3) Mark angle.
Baseline
on zero degrees
Draw a 58 angle that opens left.
Steps
1) Draw baseline.
Vertex in
center of hole
Draw a 136 angle that opens left.
Steps
1) Draw baseline.
2) Line up
pprotractor.
3) Mark angle.
4) Draw ray.
5) Label angle
measure.
58
If angle < 90 , it should
look acute.
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
3
Lesson 1-3
Draw a 136 angle that opens left.
Draw a 136 angle that opens left.
Steps
1) Draw baseline.
Steps
1) Draw baseline.
2) Line up
pprotractor.
2) Line up
pprotractor.
3) Mark angle.
3) Mark angle.
4) Draw ray.
136
5) Label angle
measure.
If angle > 90 , it should
look obtuse.
Baseline
on zero degrees
Vertex in
center of hole
Constructing a Congruent Angle
Constructing a Congruent Angle
Construct X congruent to A .
Construct X congruent to A .
A
A
X
X
Constructing a Congruent Angle
Constructing a Congruent Angle
Construct X congruent to A .
Construct X congruent to A .
A
A
X
X
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
4
Lesson 1-3
Constructing a Congruent Angle
Construct X congruent to A .
Angle Addition Postulate
If N is in the interior of ABC, then
mABN  mNBC  mABC.
A
N
B
A
C
If Z lies in the interior of XYK, mXYZ  45
and mZYK  80, find mXYK.
mXYZ  mZYK  mXYK
X 45 Z
45 + 80  125
80
mXYK  125
Y
K
X
G lies in the interior of EFH. If mEFG  36
and mEFH=120, find mGFH.
E
mEFG  mGFH  mEFH
G
F
Constructing an Angle Bisector
H
36  mGFH  120
36
 36
mGFH  84
Constructing an Angle Bisector
Constructing an Angle Bisector
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
5
Lesson 1-3
Constructing an Angle Bisector
Constructing an Angle Bisector
Constructing an Angle Bisector
Constructing an Angle Bisector
Constructing an Angle Bisector

AB bisects DAC, mDAB  (5x  30),
mBAC  (2x  63), find mDAC.
D 5x  30
B
mDAB  5x  30
2x  63
 5(11)  30
A
C
mDAB  85
mDAB  mBAC
(5x  30) (2x  63)
mDAC  2mDAB
2x
 2x
 2(85)
3x  30  63
mDAC  170
30  30
3x  33
x  11
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
6