Download 9-3 Arcs and Central Angles

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Problem of Apollonius wikipedia, lookup

Multilateration wikipedia, lookup

Pythagorean theorem wikipedia, lookup

Rational trigonometry wikipedia, lookup

Euler angles wikipedia, lookup

Trigonometric functions wikipedia, lookup

Geometrization conjecture wikipedia, lookup

Line (geometry) wikipedia, lookup

History of geometry wikipedia, lookup

History of trigonometry wikipedia, lookup

Euclidean geometry wikipedia, lookup

Transcript
Honors Geometry_9.3_March 2
Warmup
1) Solve for x.
C is center
P is point of tangency
6
C
x
8
2) Solve for x and y.
P
Both the Blue line and purple line
8
Revisit THEOREM 9.1 if necessary
are tangent to the circle
x
18
y
18
60˚
9-3
Arcs and Central Angles
I can ... explain how to find the measure of a given arc or a given
central angle.
I can... solve real world problems involving central angles and
arcs of circles. [G.CO.1, G.C.2]
1
Honors Geometry_9.3_March 2
CENTRAL ANGLE - an angle with its vertex at the center of the
circle & whose two sides are radii.
ARC - portion of the edge of the circle defined by two endpoints.
MINOR ARC
- arc that is in the interior of the central ∠.
- measure will be less than 180˚.
- Use 2 letters to name.
MAJOR ARC
- arc with a measure greater than 180˚
- Use 3 letters to name.
SEMICIRCLE
- arc with endpoints on the diameter.
- measure equals 180˚.
- Use 3 letters to name.
MEASURING ARCS
Measures of arcs are related to corresponding central angles.
measure of a minor arc - the measure of its central angle
measure of a major arc - 360˚ minus the measure of the minor arc.
measure of a semicircle - 180˚
2
Honors Geometry_9.3_March 2
Two arcs of the same circle are adjacent if they intersect at
exactly 1 point. You can add the measures of adjacent angles using...
Arc Addition Postulate:
The measure of the arc formed by 2 adjacent arcs is the sum of
the measures of the 2 arcs.
Two arcs of the same circle or of congruent circles are congruent
arcs if they have the same measure.
Theorem 9.3
In the same circle or in congruent circles, 2 minor arcs are
congruent if and only if their central angles are congruent.
50o
50o
3
Honors Geometry_9.3_March 2
Name the following: (O is the center)
a) two minor arcs
b) two major arcs
c) two semicircles
C
,
, etc.
R
O
d) an acute central angle
S
A
e) two congruent arcs
Give the measure of each angle or arc. YT is a diameter.
a) mWX = _______
b) mXY = _______
Y
X
30 o
c) m∠WOT = _______
d) mYZT = _______
e) m∠YOT = _______
O
Z
W
50
o
T
f) mXYT = _______
4
Honors Geometry_9.3_March 2
Find:
D
E
4
-1
x
2
4x
2x
3
3x x+1
0
A) mAB = _____
C
B) mEDB = ______
B
A
[first find 'x']
Assignment P. 341 CE 1-13; WE 2-6 even; 7, 8, 10, 11, 16
5
Honors Geometry_9.3_March 2
9.3 Assignment: P. 341 CE 1-13; WE 2-6 even; 7, 8, 10, 11, 16
150˚
6
Honors Geometry_9.3_March 2
7
Honors Geometry_9.3_March 2
Answers
2)80
4) 50
6) 55
7) 30
8) 4,8
10)
60
30
11)
16) 35
70, 70
2n
3k
56 50 2x
70
50 2x
35 28
#10 & 11 HINT:
Make isosceles triangles
34 44
100 88
104 p + q
50 44 50
1/2(p+q)
8