11x1 t07 02 triangle theorems (2010)
TRANSCRIPT
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Triangle Theorems
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Triangle Theorems180 is leany triang of sum angle The
A
B
C
![Page 3: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/3.jpg)
Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
![Page 4: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/4.jpg)
Triangle Theorems180 is leany triang of sum angle The
180 sum 180 ABCCBA
A
B
C
Proof:
![Page 5: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/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: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/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: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/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: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/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
![Page 9: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/9.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 DAECAEBACDAB180 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
![Page 13: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/13.jpg)
A
B
CD
CABBAACD ,exterior
The exterior angle of any triangle is equal to the sum of the two opposite interior angles
Proof:
![Page 14: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/14.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
E
![Page 15: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/15.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
![Page 16: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/16.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
![Page 17: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/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
![Page 18: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/18.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
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: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/22.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof:
![Page 23: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/23.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof:
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Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
![Page 25: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/25.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
![Page 26: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/26.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
360sum ABCD
![Page 27: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/27.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
360sum ABCD
A
B
C
DE
![Page 28: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/28.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
360sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
![Page 29: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/29.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
360sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBA
![Page 30: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/30.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
360sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBAProof:
![Page 31: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/31.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
360sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBAProof:
![Page 32: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/32.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
360sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBAProof: 180sum ABE
![Page 33: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/33.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
360sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBAProof: 180sum ABE
180sum BED
![Page 34: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/34.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
360sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBAProof: 180sum ABE
180sum BED(+)
180sum BDC
![Page 35: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/35.jpg)
Polygon TheoremsA B
CD
360 is ralquadrilateany of sum angle The
360 sum 360 ABCDDCBAProof: 180sum ABC
180sum ADC(+)
360sum ABCD
A
B
C
DE
540 ispentagon any of sum angle The
540 sum 540 ABCDEEDCBAProof: 180sum ABE
180sum BED(+)
540sum ABCDE
180sum BDC
![Page 36: 11X1 T07 02 triangle theorems (2010)](https://reader034.vdocuments.us/reader034/viewer/2022052602/559c917b1a28ab525b8b46d7/html5/thumbnails/36.jpg)
sidesofnumber theis where
,2180 ispolygon any of sum angle Then
n-
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sidesofnumber theis where
,2180 ispolygon any of sum angle Then
n-
a
b
cd
e
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sidesofnumber theis where
,2180 ispolygon any of sum angle Then
n-
a
b
cd
e
360 ispolygon any ofsumangleexterior The
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sidesofnumber theis where
,2180 ispolygon any of sum angle Then
n-
a
b
cd
e
360 ispolygon any ofsumangleexterior The
360sum exterior 360 edcba
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sidesofnumber theis where
,2180 ispolygon any of sum angle Then
n-
a
b
cd
e
360 ispolygon any ofsumangleexterior The
360sum exterior 360 edcba
Exercise 8B; 1dg, 2c, 3dh, 5ace, 6ab (iii), 7b, 8bfh, 9ad, 10dh,11ad, 12c, 16, 18, 20