11 x1 t13 03 angle theorems 2 (2013)
TRANSCRIPT
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Angle Theorems
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Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
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Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
C
A
B
O
D
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Angle Theorems (5b) Opposite angles of a cyclic quadrilateral are supplementary.
180 ralquadrilate cyclicin s'opposite 180 ADCABC
C
A
B
O
D
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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
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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
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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
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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
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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
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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
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(5c) The exterior angle of a cyclic quadrilateral is equal to the
opposite interior angle.
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(5c) The exterior angle of a cyclic quadrilateral is equal to the
opposite interior angle.
C
A
B
O
D
X
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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
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(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
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(6) Angles subtended at the circumference by the same or equal arcs
(or chords) are equal.
A
B
O
C
D
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(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
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(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
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(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
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(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
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(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
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(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
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(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