11 X1 T06 02 Triangle Theorems

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