11X1 T07 02 triangle theorems (2010)

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• 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 ABCCBAA

B

C

• Triangle Theorems180 is leany triang of sum angle The

180 sum 180 ABCCBAA

B

C

Proof:

• Triangle Theorems180 is leany triang of sum angle The

180 sum 180 ABCCBAA

B

C

Proof:Construct DE||BC passing through A

D

E

• Triangle Theorems180 is leany triang of sum angle The

180 sum 180 ABCCBAA

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 ABCCBAA

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 ABCCBAA

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 ABCCBAA

B

C

Proof:Construct DE||BC passing through A

D

E

BCDEABCDAB ||,s'alternate BCDEACBEAC ||,s'alternate 180straight 180 DAECAEBACDAB

180 ACBBACABC

• AB

CD

• AB

CD

The exterior angle of any triangle is equal to the sum of the two opposite interior angles

• AB

CD

CABBAACD ,exterior

The exterior angle of any triangle is equal to the sum of the two opposite interior angles

• AB

CD

CABBAACD ,exterior

The exterior angle of any triangle is equal to the sum of the two opposite interior angles

Proof:

• AB

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

• AB

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

• AB

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

• AB

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

• AB

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 ABCDDCBAProof:

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof:

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

360sum ABCD

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

360sum ABCD

A

B

C

DE

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

360sum 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 ABCDDCBAProof: 180sum ABC

360sum 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 ABCDDCBAProof: 180sum ABC

360sum ABCD

A

B

C

DE

540 ispentagon any of sum angle The

540 sum 540 ABCDEEDCBAProof:

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

360sum ABCD

A

B

C

DE

540 ispentagon any of sum angle The

540 sum 540 ABCDEEDCBAProof:

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

360sum ABCD

A

B

C

DE

540 ispentagon any of sum angle The

540 sum 540 ABCDEEDCBAProof: 180sum ABE

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

360sum ABCD

A

B

C

DE

540 ispentagon any of sum angle The

540 sum 540 ABCDEEDCBAProof: 180sum ABE

180sum BED

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

360sum ABCD

A

B

C

DE

540 ispentagon any of sum angle The

540 sum 540 ABCDEEDCBAProof: 180sum ABE

180sum BED(+)

180sum BDC

• Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

360sum ABCD

A

B

C

DE

540 ispentagon any of sum angle The

540 sum 540 ABCDEEDCBAProof: 180sum ABE

180sum BED(+)

540sum ABCDE180sum BDC

• sidesofnumber theis where

,2180 ispolygon any of sum angle Then

n-

• sidesofnumber theis where

,2180 ispolygon any of sum angle Then

n-

a

b

cd

e

• sidesofnumber theis where

,2180 ispolygon any of sum angle Then

n-

a

b

cd

e

360 ispolygon any ofsumangleexterior The

• sidesofnumber theis where

,2180 ispolygon any of sum angle Then

n-

a

b

cd

e

360 ispolygon any ofsumangleexterior The

360sum exterior 360 edcba

• sidesofnumber theis where

,2180 ispolygon any of sum angle Then

n-

a

b

cd

e

360 ispolygon any ofsumangleexterior The

360sum exterior 360 edcbaExercise 8B; 1dg, 2c, 3dh, 5ace, 6ab (iii), 7b, 8bfh, 9ad, 10dh,