Download - CCGPS Geometry Day 41 ( 3-24-14 )
![Page 1: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/1.jpg)
CCGPS GeometryDay 41 (3-24-14)
UNIT QUESTION: What special properties are found with the parts of a circle?Standard: MMC9-12.G.C.1-5,G.GMD.1-3
Today’s Question:How do we use angle measures to find measures of arcs?Standard: MMC9-12.G.C.2
![Page 2: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/2.jpg)
AGENDA1. Notes on Circles2. Notes on Central
Angles3. Practice Worksheet4. Homework
Worksheet
![Page 3: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/3.jpg)
![Page 4: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/4.jpg)
![Page 5: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/5.jpg)
Parts of a Circle
Circle – set of all points _________ from a given point called the _____ of the circle.
C
Symbol:
equidistant
center
C
![Page 6: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/6.jpg)
CHORD:A segment whose endpoints are on the circle
![Page 7: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/7.jpg)
P
RADIUS:Distance from the center to point on circle
Radius
![Page 8: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/8.jpg)
Diameter
P
DIAMETER:Distance across the circle through its center
Also known as the longest chord.
![Page 9: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/9.jpg)
D = ?
r = ?
r = ? D = ?
![Page 10: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/10.jpg)
Use P to determine whether each statement is true or false.
P
Q
R
TS
diameter. a is .1 RT False
radius. a is .2 PS True
chord. a is .3 QT True
![Page 11: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/11.jpg)
Secant Line:intersects the circle at exactly TWO points
![Page 12: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/12.jpg)
a LINE that intersects the circle exactly
ONE time
Tangent Line:
Forms a 90°angle with a radiusPoint of Tangency: The point where the tangent intersects the circle
![Page 13: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/13.jpg)
Name the term that best describes the notation.
Secant
Radius
DiameterChord
Tangent
![Page 14: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/14.jpg)
![Page 15: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/15.jpg)
P
A
BC
Central Angle : An Angle whose vertex is at the center of the
circleMinor ArcMajor Arc
Less than 180°
More than 180°
ABACB
To name: use 2 letters
To name: use 3 letters
APB is a Central Angle
![Page 16: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/16.jpg)
P
E
F
D
Semicircle: An Arc that equals 180°
EDF
To name: use 3 letters
![Page 17: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/17.jpg)
THINGS TO KNOW AND REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
![Page 18: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/18.jpg)
measure of an arc = measure of central angle
A
B
C
Q 96
m AB
m ACB
m AE
E
=
=
=
96°
264°
84°
![Page 19: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/19.jpg)
Arc Addition PostulateA
B
C
m ABC =
m AB + m BC
![Page 20: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/20.jpg)
Tell me the measure of the following arcs.
80100
40
140A
B
C
D
R
m DAB =
m BCA =
240
260
![Page 21: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/21.jpg)
Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles.
4545
A
BC
D
110
Arc length is proportional to “r”
![Page 22: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/22.jpg)
Classwork
• Practice Worksheet
![Page 23: CCGPS Geometry Day 41 ( 3-24-14 )](https://reader035.vdocuments.net/reader035/viewer/2022062221/56813cbb550346895da666bf/html5/thumbnails/23.jpg)
Homework:
• Practice Worksheet