are diameters. find the indicated measures. 1) 2) 3) 4)
TRANSCRIPT
and KM LN
mOL
m OPM
mNOL
mONM
50°
75°
K L
MN
0
P
are diameters. Find the indicated measures.
1)
2)
3)
4)
Warm-up
50
A
B
C
MN
P
1. Let AM = 8, BP = 7, and CA = 18. Find the perimeter of the triangle.
24
A
B
C
2. Find ACB
3. MCY = 270 Find BC.
20
M B
Y C
90
31220
Math II
UNIT QUESTION: What special properties are found with the parts of a circle?Standard: MM2G1, MM2G2
Today’s Question:What other angle relationships do we know for circles?Standard: MM2G3.b
6.5 Other Angles in a Circle
Case I: Vertex is ON the circle
ANGLE = ARC
2ANGLE
ARCANGLE
ARC
Ex. 1 Find m1. AB
C124°
1
m1 = 62
Ex. 2 Find m1.
84°
1
m1 = 42
Ex. 3 Find m1. 202°
1
m1 = 79
Case II: Vertex is inside the circleA
B
C
D
ANGLE = (ARC + ARC)
2
ANGLE
ARC
ARC
Ex. 4 Find m1.A
B
CD
1
93°
113°
m1 = 103
Ex. 5 Find mQT.N
Q
TM
9284
mQT = 100
Homework:Workbook
p. 225 #1-9p. 226 #17-19
Case III: Vertex is outside the circle
A
B
C
D
ANGLE = (Large ARC Small ARC)
2
ANGLE
LA
RGE
AR
C
small
ARC
ANGLELA
RG
E
AR
C
sm
all A
RC
small A
RC
LARGE
ARC
AN
GL
E
A
B
D
1
Ex. 6 Find m1.
65°
15°
m<1 = 25 degrees
A
B
Ex. 7 Find mAB.
27°
70°
mAB = 16 degrees
1
Ex. 8 Find m1.26
0°
m<1 = 80 degrees
ClassworkWorkbook p. 225 #10-16; p. 227
#20, 21Homework:
Textbook p. 208 #19, 20; p. 214
#1-12