ccgps geometry day 41 ( 3-24-14 )
DESCRIPTION
CCGPS Geometry Day 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. AGENDA. Notes on Circles - PowerPoint PPT PresentationTRANSCRIPT
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
AGENDA1. Notes on Circles2. Notes on Central
Angles3. Practice Worksheet4. Homework
Worksheet
Parts of a Circle
Circle – set of all points _________ from a given point called the _____ of the circle.
C
Symbol:
equidistant
center
C
CHORD:A segment whose endpoints are on the circle
P
RADIUS:Distance from the center to point on circle
Radius
Diameter
P
DIAMETER:Distance across the circle through its center
Also known as the longest chord.
D = ?
r = ?
r = ? D = ?
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
Secant Line:intersects the circle at exactly TWO points
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
Name the term that best describes the notation.
Secant
Radius
DiameterChord
Tangent
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
P
E
F
D
Semicircle: An Arc that equals 180°
EDF
To name: use 3 letters
THINGS TO KNOW AND REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
measure of an arc = measure of central angle
A
B
C
Q 96
m AB
m ACB
m AE
E
=
=
=
96°
264°
84°
Arc Addition PostulateA
B
C
m ABC =
m AB + m BC
Tell me the measure of the following arcs.
80100
40
140A
B
C
D
R
m DAB =
m BCA =
240
260
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”
Classwork
• Practice Worksheet
Homework:
• Practice Worksheet