11 x1 t06 02 triangle theorems
TRANSCRIPT
Triangle Theorems
Triangle Theorems180 is leany triang of sum angle The
A
B
C
Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
Proof:
Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
Proof:Construct DE||BC passing through A
D
E
Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
Proof:Construct DE||BC passing through A
D
E
BCDEABCDAB ||,s' alternate
Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
Proof:Construct DE||BC passing through A
D
E
BCDEABCDAB ||,s' alternate
BCDEACBEAC ||,s' alternate
Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
Proof:Construct DE||BC passing through A
D
E
BCDEABCDAB ||,s' alternate
BCDEACBEAC ||,s' alternate
180straight 180 DAECAEBACDAB
Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
Proof:Construct DE||BC passing through A
D
E
BCDEABCDAB ||,s' alternate
BCDEACBEAC ||,s' alternate
180straight 180 DAECAEBACDAB
180 ACBBACABC
A
B
CD
A
B
CD
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
A
B
CD
CABBAACD ,exterior
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
A
B
CD
CABBAACD ,exterior
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
Proof:
A
B
CD
CABBAACD ,exterior
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
Proof:Construct CE||BA
E
A
B
CD
CABBAACD ,exterior
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
Proof:Construct CE||BA
BACEECDABC ||,s' ingcorrespond
E
A
B
CD
CABBAACD ,exterior
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
Proof:Construct CE||BA
BACEECDABC ||,s' ingcorrespond
E
BACEACEBAC ||,s' alternate
A
B
CD
CABBAACD ,exterior
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
Proof:Construct CE||BA
BACEECDABC ||,s' ingcorrespond
E
BACEACEBAC ||,s' alternate
common ECDACEACD
A
B
CD
CABBAACD ,exterior
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
Proof:Construct CE||BA
BACEECDABC ||,s' ingcorrespond
E
BACEACEBAC ||,s' alternate
common ECDACEACD
BACABCACD
Polygon TheoremsA B
CD
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof:
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof:
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
A
B
C
DE
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBA
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBA
Proof:
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBA
Proof:
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBA
Proof: 180 sum ABE
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBA
Proof: 180 sum ABE180 sum BED
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBA
Proof: 180 sum ABE180 sum BED
(+)
180 sum BDC
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBA
Proof: 180 sum ABE180 sum BED
(+)
540 sum ABCDE
180 sum BDC
sides ofnumber theis where
,2180 ispolygon any of sum angle The
n
n-
sides ofnumber theis where
,2180 ispolygon any of sum angle The
n
n-
a
b
c
d
e
sides ofnumber theis where
,2180 ispolygon any of sum angle The
n
n-
a
b
c
d
e
360 ispolygon any
of sum angleexterior The
sides ofnumber theis where
,2180 ispolygon any of sum angle The
n
n-
a
b
c
d
e
360 ispolygon any
of sum angleexterior The
360sum exterior 360 edcba
sides ofnumber theis where
,2180 ispolygon any of sum angle The
n
n-
a
b
c
d
e
360 ispolygon any
of sum angleexterior The
360sum exterior 360 edcba
Exercise 8B; 1dg, 2c, 3dh, 5ace, 6ab (iii), 7b, 8bfh, 9ad, 10dh,11ad, 12c, 16, 18, 20