11X1 T08 02 triangle theorems (2011)

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 DAECAEBACDAB180 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 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

180sum ADC(+)

Polygon TheoremsA B

CD

360 is ralquadrilateany of sum angle The

360 sum 360 ABCDDCBAProof: 180sum ABC

180sum ADC(+)

360sum ABCD

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

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

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

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:

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:

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

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

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

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

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 edcba

Exercise 8B; 1dg, 2c, 3dh, 5ace, 6ab (iii), 7b, 8bfh, 9ad, 10dh,11ad, 12c, 16, 18, 20