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

    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 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,

    11ad, 12c, 16, 18, 20

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