11 x1 t06 02 triangle theorems
TRANSCRIPT
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Triangle Theorems
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Triangle Theorems180 is leany triang of sum angle The
A
B
C
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Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
![Page 4: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/4.jpg)
Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
Proof:
![Page 5: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/5.jpg)
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
![Page 6: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/6.jpg)
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
![Page 7: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/7.jpg)
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
![Page 8: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/8.jpg)
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
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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
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A
B
CD
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A
B
CD
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
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A
B
CD
CABBAACD ,exterior
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
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A
B
CD
CABBAACD ,exterior
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
Proof:
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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
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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
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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
![Page 17: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/17.jpg)
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
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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
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Polygon TheoremsA B
CD
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Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
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Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
![Page 22: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/22.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof:
![Page 23: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/23.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof:
![Page 24: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/24.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC
![Page 25: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/25.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
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Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBA
Proof: 180 sum ABC180 sum ADC
(+)
360 sum ABCD
![Page 27: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/27.jpg)
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
![Page 28: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/28.jpg)
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
![Page 29: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/29.jpg)
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
![Page 30: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/30.jpg)
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:
![Page 31: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/31.jpg)
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:
![Page 32: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/32.jpg)
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
![Page 33: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/33.jpg)
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
![Page 34: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/34.jpg)
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
![Page 35: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/35.jpg)
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
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sides ofnumber theis where
,2180 ispolygon any of sum angle The
n
n-
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sides ofnumber theis where
,2180 ispolygon any of sum angle The
n
n-
a
b
c
d
e
![Page 38: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/38.jpg)
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
![Page 39: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/39.jpg)
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
![Page 40: 11 X1 T06 02 Triangle Theorems](https://reader035.vdocuments.us/reader035/viewer/2022081516/55873726d8b42a18238b4626/html5/thumbnails/40.jpg)
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