11x1 t13 03 angle theorems 2 (2011)
TRANSCRIPT
Angle Theorems
Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
C
A
B
O
D
Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
180 ralquadrilate cyclicin s'opposite 180 ADCABC
C
A
B
O
D
Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
180 ralquadrilate cyclicin s'opposite 180 ADCABC
180 :Prove
C
A
B
O
D
Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
180 ralquadrilate cyclicin s'opposite 180 ADCABC
180 :Prove Proof: Join AO and CO
C
A
B
O
D
Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
180 ralquadrilate cyclicin s'opposite 180 ADCABC
180 :Prove Proof: Join AO and CO
arc samenceon circumfere
at twicecentreat 2αAOC
C
A
B
O
D
Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
180 ralquadrilate cyclicin s'opposite 180 ADCABC
180 :Prove Proof: Join AO and CO
arc samenceon circumfere
at twicecentreat 2αAOC
C
A
B
O
D
arc samenceon circumfere
at twicecentreat 2reflexAOC
Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
180 ralquadrilate cyclicin s'opposite 180 ADCABC
180 :Prove Proof: Join AO and CO
arc samenceon circumfere
at twicecentreat 2αAOC
revolution 36022 reflexAOCAOC
C
A
B
O
D
arc samenceon circumfere
at twicecentreat 2reflexAOC
Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
180 ralquadrilate cyclicin s'opposite 180 ADCABC
180 :Prove Proof: Join AO and CO
arc samenceon circumfere
at twicecentreat 2αAOC
revolution 36022 reflexAOCAOC
180
C
A
B
O
D
arc samenceon circumfere
at twicecentreat 2reflexAOC
(5c) The exterior angle of a cyclic quadrilateral is equal to the
opposite interior angle.
(5c) The exterior angle of a cyclic quadrilateral is equal to the
opposite interior angle.
C
A
B
O
D
X
interior opposite
alquadilater cyclicexterior BADDCX
(5c) The exterior angle of a cyclic quadrilateral is equal to the
opposite interior angle.
C
A
B
O
D
X
(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
A
B
O
C
D
(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
aresegment samein s' ACDABD
A
B
O
C
D
(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
aresegment samein s' ACDABD
ACDABD :Prove
A
B
O
C
D
(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
aresegment samein s' ACDABD
ACDABD :Prove
Proof: Join AO and DO
A
B
O
C
D
(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
aresegment samein s' ACDABD
ACDABD :Prove
Proof: Join AO and DO
arc sameon ncecircumfere
at twicecentreat 2 ABDAOD
A
B
O
C
D
(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
aresegment samein s' ACDABD
ACDABD :Prove
Proof: Join AO and DO
arc sameon ncecircumfere
at twicecentreat 2 ABDAOD
A
B
O
C
D
arc sameon ncecircumfere
at twicecentreat 2 ACDAOD
(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
aresegment samein s' ACDABD
ACDABD :Prove
Proof: Join AO and DO
arc sameon ncecircumfere
at twicecentreat 2 ABDAOD
ACDABD
A
B
O
C
D
arc sameon ncecircumfere
at twicecentreat 2 ACDAOD
(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
aresegment samein s' ACDABD
ACDABD :Prove
Proof: Join AO and DO
arc sameon ncecircumfere
at twicecentreat 2 ABDAOD
ACDABD
Exercise 9C; 1 ace etc, 2 aceg, 3, 4 bd, 6 bdf, 7 bdf, 9, 13, 14
A
B
O
C
D
arc sameon ncecircumfere
at twicecentreat 2 ACDAOD