Download Cyclic Quadrilaterals

3
LESSON 43
Cyclic Quadrilaterals
MPM2D | MCR3U
IB MYP 5 MATHEMATICS EXTENDED
IB CONTENTS
LESSON PLAN
Geometry and
Trigonometry
D
E
F
I
Haese & Harris
N
I
T
I
O
N

Concyclic

Cyclic quadrilateral
21.D
Cyclic Quadrilaterals
S
ONTARIO EXPECTATIONS
TEXTBOOK
Prepared by Dr. Benedict Hung
Haese & Harris
Pg. 521 - Pg. 526
KEY TERMS
concyclic, cyclic
quadrilateral,
supplementary angles
T
H
E
O
R
E
M
Opposite Angles of a Cyclic Quadrilateral Theorem

the opposite angles of a cyclic
quadrilateral are supplementary

FORMULAE & STATEMENTS
D
180o-y
A
N
O
T
E
x C
O
180o-x
y
B
S
A circle can always be drawn through any three points that are not
collinear. However, a circle may or may not be drawn through four or
more points in a plane.
A quadrilateral is cyclic if-and-only-if any of its exterior angles is equal to
the interior and opposite angle.


E
X
A
M
P
L
E
1
Find x

D
x
70o
C
B
A
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
C
A
N
A
D
I
A
N
I
N
T
E
R
N
A
T
I
O
N
A
L
S
C
H
O
O
L
O
F
H
O
N
G
K
O
N
G
E

X
A
M
P
L
E
Find x and y
2
E
D
70o
C
y
A x
B
Prepared by Dr. Benedict Hung
ASSIGNMENT
Haese & Harris
2
Pg. 523 # 1, 3, 7, 9, 10, 12, 13, 15
IB MYP 5 Mathematics Extended  MPM2D  MCR3U  Unit 3 – Coordinate Geometry