11 x1 t07 01 angle theorems (2013)

Download 11 x1 t07 01 angle theorems (2013)

Post on 08-Jul-2015

226 views

Category:

Education

0 download

Embed Size (px)

TRANSCRIPT

  • Euclidean Geometry

  • Euclidean Geometry Geometry Definitions

    Notation

    toparallel is ||

  • Euclidean Geometry Geometry Definitions

    Notation

    toparallel is ||

    lar toperpendicu is

  • Euclidean Geometry Geometry Definitions

    Notation

    toparallel is ||

    lar toperpendicu is

    tocongruent is

  • Euclidean Geometry Geometry Definitions

    Notation

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

  • Euclidean Geometry Geometry Definitions

    Notation

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

    therefore

  • Euclidean Geometry Geometry Definitions

    Notation

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

    therefore

    because

  • Euclidean Geometry Geometry Definitions

    Notation

    Terminology

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

    therefore

    because

    produced the line is extended

  • Euclidean Geometry Geometry Definitions

    Notation

    Terminology

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

    therefore

    because

    produced the line is extended

    X Y XY is produced to A

    A

  • Euclidean Geometry Geometry Definitions

    Notation

    Terminology

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

    therefore

    because

    produced the line is extended

    X Y XY is produced to A

    A

    YX is produced to B

    B

  • Euclidean Geometry Geometry Definitions

    Notation

    Terminology

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

    therefore

    because

    produced the line is extended

    X Y XY is produced to A

    A

    YX is produced to B

    B

    foot the base or the bottom

  • Euclidean Geometry Geometry Definitions

    Notation

    Terminology

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

    therefore

    because

    produced the line is extended

    X Y XY is produced to A

    A

    YX is produced to B

    B

    foot the base or the bottom

    A B

    C D

    B is the foot of the perpendicular

  • Euclidean Geometry Geometry Definitions

    Notation

    Terminology

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

    therefore

    because

    produced the line is extended

    X Y XY is produced to A

    A

    YX is produced to B

    B

    foot the base or the bottom

    A B

    C D

    B is the foot of the perpendicular

    collinear the points lie on the same line

  • Euclidean Geometry Geometry Definitions

    Notation

    Terminology

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

    therefore

    because

    produced the line is extended

    X Y XY is produced to A

    A

    YX is produced to B

    B

    foot the base or the bottom

    A B

    C D

    B is the foot of the perpendicular

    collinear the points lie on the same line

    concurrent the lines intersect at the same

    point

  • Euclidean Geometry Geometry Definitions

    Notation

    Terminology

    toparallel is ||

    lar toperpendicu is

    tocongruent is

    similar to is |||

    therefore

    because

    produced the line is extended

    X Y XY is produced to A

    A

    YX is produced to B

    B

    foot the base or the bottom

    A B

    C D

    B is the foot of the perpendicular

    collinear the points lie on the same line

    concurrent the lines intersect at the same

    point transversal a line that cuts two(or more)

    other lines

  • Naming Conventions

    Angles and Polygons are named in cyclic order

  • Naming Conventions

    Angles and Polygons are named in cyclic order

    A

    B C

    CBAABC or

    BB or

    ambiguity no If

  • Naming Conventions

    Angles and Polygons are named in cyclic order

    A

    B C

    CBAABC or

    BB or

    ambiguity no If

    P

    V

    T

    Q

    VPQT or QPVT

    or QTVP etc

  • Naming Conventions

    Angles and Polygons are named in cyclic order

    A

    B C

    CBAABC or

    BB or

    ambiguity no If

    P

    V

    T

    Q

    VPQT or QPVT

    or QTVP etc

    Parallel Lines are named in corresponding order

  • Naming Conventions

    Angles and Polygons are named in cyclic order

    A

    B C

    CBAABC or

    BB or

    ambiguity no If

    P

    V

    T

    Q

    VPQT or QPVT

    or QTVP etc

    Parallel Lines are named in corresponding order

    A

    B

    C

    D

    AB||CD

  • Naming Conventions

    Angles and Polygons are named in cyclic order

    A

    B C

    CBAABC or

    BB or

    ambiguity no If

    P

    V

    T

    Q

    VPQT or QPVT

    or QTVP etc

    Parallel Lines are named in corresponding order

    A

    B

    C

    D

    AB||CD

    Equal Lines are marked with the same symbol

  • Naming Conventions

    Angles and Polygons are named in cyclic order

    A

    B C

    CBAABC or

    BB or

    ambiguity no If

    P

    V

    T

    Q

    VPQT or QPVT

    or QTVP etc

    Parallel Lines are named in corresponding order

    A

    B

    C

    D

    AB||CD

    Equal Lines are marked with the same symbol

    P

    Q R

    S

    PQ = SR

    PS = QR

  • Constructing Proofs

    When constructing a proof, any line that you state must be one of the

    following;

  • Constructing Proofs

    When constructing a proof, any line that you state must be one of the

    following;

    1. Given information, do not assume information is given, e.g. if you

    are told two sides are of a triangle are equal dont assume it is

    isosceles, state that it is isosceles because two sides are equal.

  • Constructing Proofs

    When constructing a proof, any line that you state must be one of the

    following;

    1. Given information, do not assume information is given, e.g. if you

    are told two sides are of a triangle are equal dont assume it is

    isosceles, state that it is isosceles because two sides are equal.

    2. Construction of new lines, state clearly your construction so that

    anyone reading your proof could recreate the construction.

  • Constructing Proofs

    When constructing a proof, any line that you state must be one of the

    following;

    1. Given information, do not assume information is given, e.g. if you

    are told two sides are of a triangle are equal dont assume it is

    isosceles, state that it is isosceles because two sides are equal.

    2. Construction of new lines, state clearly your construction so that

    anyone reading your proof could recreate the construction.

    3. A recognised geometrical theorem (or assumption), any theorem

    you are using must be explicitly stated, whether it is in the algebraic

    statement or the reason itself.

  • Constructing Proofs

    When constructing a proof, any line that you state must be one of the

    following;

    1. Given information, do not assume information is given, e.g. if you

    are told two sides are of a triangle are equal dont assume it is

    isosceles, state that it is isosceles because two sides are equal.

    2. Construction of new lines, state clearly your construction so that

    anyone reading your proof could recreate the construction.

    3. A recognised geometrical theorem (or assumption), any theorem

    you are using must be explicitly stated, whether it is in the algebraic

    statement or the reason itself.

    180 sum 18012025 e.g. A

  • Constructing Proofs

    When constructing a proof, any line that you state must be one of the

    following;

    1. Given information, do not assume information is given, e.g. if you

    are told two sides are of a triangle are equal dont assume it is

    isosceles, state that it is isosceles because two sides are equal.

    2. Construction of new lines, state clearly your construction so that

    anyone reading your proof could recreate the construction.

    3. A recognised geometrical theorem (or assumption), any theorem

    you are using must be explicitly stated, whether it is in the algebraic

    statement or the reason itself.

    180 sum 18012025 e.g. A

    Your reasoning should be clear and concise

  • Constructing Proofs

    When constructing a proof, any line that you state must be one of the

    following;

    1. Given information, do not assume information is given, e.g. if you

    are told two sides are of a triangle are equal dont assume it is

    isosceles, state that it is isosceles because two sides are equal.

    2. Constru