Take out a piece of paper for notes
description
Transcript of Take out a piece of paper for notes
![Page 1: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/1.jpg)
![Page 2: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/2.jpg)
![Page 3: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/3.jpg)
RayRay
An object that has one endpoint and continues
infinitely in ONE direction.
![Page 4: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/4.jpg)
AngleAngle
An object that has two rays (called sides) with
a common endpoint (called the vertex).
![Page 5: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/5.jpg)
Example 1
Name each of the following:
Sides:_____________________
Vertex:_________
Name:_____________________
A
B
C
![Page 6: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/6.jpg)
Interior of an AngleInterior of an Angle
the space between the rays that create an
angle.
![Page 7: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/7.jpg)
Exterior of an AngleExterior of an Angle
the space that is outside of the rays
![Page 8: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/8.jpg)
Example 2
How does the diagram in EXAMPLE 1 differ from the diagram in this example?
Q
P
R
S
![Page 9: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/9.jpg)
Example 3
A) Name a point in the interior of QPS in EXAMPLE 2.
B) Name a point in the exterior of QPR in EXAMPLE 2.
Q
P
R
S
![Page 10: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/10.jpg)
AdjacentAdjacent
To be next to.
SHARING a side.
![Page 11: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/11.jpg)
Angle Addition PostulateAngle Addition Postulate
The sum of two adjacent angles is equal to the
largest angle.
![Page 12: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/12.jpg)
ANGLE ADDITION POSTULATE:
Q
P
R
S
If R is in the interior of QPS, then mQPR + mRPS = mQPS.
If mQPR + mRPS = mQPS, then R is in the interior of QPS.
![Page 13: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/13.jpg)
ANGLE ADDITION POSTULATE:
Q
P
R
S
If R is in the interior of QPS, then mQPR + mRPS = mQPS.
If mQPR + mRPS = mQPS, then R is in the interior of QPS.
![Page 14: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/14.jpg)
Example 4
If mPQS = 77 and mPQR = 32, then find mRQS.
P
Q
R
S
![Page 15: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/15.jpg)
Example 5
If mAOC = 70, mAOB =(x + 10), and mBOC =x, find:
x = __________
mBOC = _______________
mAOB = _______________
O
A
B
C
![Page 16: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/16.jpg)
Angles can be classified by their measure in degrees.
If an angle has a degree measure less than 90° it is classified as an _acute angle__.
If an angle has a degree measure equal to 90° it is classified as a __ right angle ____.
![Page 17: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/17.jpg)
Acute AngleAcute Angle
An angle measuring
less than 90°
![Page 18: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/18.jpg)
Right AngleRight Angle
An angle whose measure is exactly 90°
![Page 19: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/19.jpg)
Obtuse AngleObtuse Angle
An angle measuring
greater than 90°
but less than 180°
![Page 20: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/20.jpg)
Straight AngleStraight Angle
An angle measuring
exactly 180°
![Page 21: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/21.jpg)
For each of the following anglesA) Name it.
B) Tell whether its measure is <90, >90, =90, or = 180. C) Classify it.
NAME:_________ OR ______MEASURE:________CLASSIFICATION___________
F
Y
I
NAME:_________ OR ______MEASURE:________CLASSIFICATION___________
T
L
C
NAME:_________ OR ______MEASURE:________CLASSIFICATION___________
T
R
S
NAME:_________ OR ______MEASURE:________CLASSIFICATION___________
N X S
35 125
![Page 22: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/22.jpg)
CongruentCongruent
to be the same shape and same size.
![Page 23: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/23.jpg)
Angle BisectorAngle Bisectora line, ray, or segment
that divides an angle into two congruent angles.
![Page 24: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/24.jpg)
Example 7
If XZ is an angle bisector of WXY, name the two congruent angles that it forms.
WX
Z
Y
![Page 25: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/25.jpg)
Example 8
FG bisects EFH. Find the value of x.
m EFG = (5x – 10); m GFH = (3x + 25)
I F H
EG
![Page 26: Take out a piece of paper for notes](https://reader035.fdocuments.net/reader035/viewer/2022062410/56815a08550346895dc755f6/html5/thumbnails/26.jpg)
Example 9
FG bisects EFH. Find the value of x.
m GFH = (3x + 20); m EFH = (4x + 80)
I F H
EG