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Math Help - Paragraph Proofs! - Geometry

  1. #1
    Junior Member Melancholy's Avatar
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    Paragraph Proofs! - Geometry

    Help... I don't know how to write a paragraph proof and my test is tommorrow. It's not my fault, I swear. I'm a good student, I just don't have a good teacher

    Write a paragraph proof.
    Given: AM = CN, MB = ND
    Prove: AB = CD

    A _____M______ B
    .______._______.
    | _____________|
    | _____________|
    .______._______.
    D _____N ______C

    (that's pretty much the drawing they give me. "." represents the points on the quadrilateral...)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Melancholy View Post
    Help... I don't know how to write a paragraph proof and my test is tommorrow. It's not my fault, I swear. I'm a good student, I just don't have a good teacher

    Write a paragraph proof.
    Given: AM = CN, MB = ND
    Prove: AB = CD

    A _____M______ B
    .______._______.
    | _____________|
    | _____________|
    .______._______.
    D _____N ______C

    (that's pretty much the drawing they give me. "." represents the points on the quadrilateral...)
    what do you mean by "paragraph proofs"?

    this can be done in one line:

    AB = AM + MB = CN + ND = CD
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  3. #3
    Junior Member Melancholy's Avatar
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    what do you mean by "paragraph proofs"?
    Instead of a formal (two-column proof) consisting of a "Statements" and "Reasons" column, the evidence is shown in a paragraph form... I suppose...

    Like for instance...

    Given that M is the midpoint of PQ, write a paragraph proof to show that PM [is congruent to] MQ.

    Given : M is the midpoint of PQ.
    Prove: PM [is congruent to] MQ

    "From he definition of a midpoint of a segment, PM = MQ. This means that PM and MQ have the same measure. By the definition of congruence, if two segments have the same measure, then they are congruent. Thus, PM [is congruent to] MQ."

    That's just an example...

    I don't need to know just the answer from the problem above...
    Write a paragraph proof.
    Given: AM = CN, MB = ND

    Prove: AB = CD

    A _____M______ B
    .______._______.
    | _____________|
    | _____________|
    .______._______.
    D _____N ______C
    ... I need to know how to get it using paragraph form.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Melancholy View Post
    Instead of a formal (two-column proof) consisting of a "Statements" and "Reasons" column, the evidence is shown in a paragraph form... I suppose...

    Like for instance...

    Given that M is the midpoint of PQ, write a paragraph proof to show that PM [is congruent to] MQ.

    Given : M is the midpoint of PQ.
    Prove: PM [is congruent to] MQ

    "From he definition of a midpoint of a segment, PM = MQ. This means that PM and MQ have the same measure. By the definition of congruence, if two segments have the same measure, then they are congruent. Thus, PM [is congruent to] MQ."

    That's just an example...

    I don't need to know just the answer from the problem above...
    ... I need to know how to get it using paragraph form.
    all you will be doing, it seems, is describing what i did in the equation i posted. try to describe it in words, i will guide you
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  5. #5
    Junior Member Melancholy's Avatar
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    I don't really know how to understand it/work it. Am I basing it off a theorem? Or a postulate? I think it would be a theorem... but I don't know.

    Would it be the segment congruence theorem?
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Melancholy View Post
    I don't really know how to understand it/work it. Am I basing it off a theorem? Or a postulate? I think it would be a theorem... but I don't know.

    Would it be the segment congruence theorem?
    well, i don't know what theorems you want to use, but the gist of what you say should be:

    since AB is composed of the segments AM and MB, we have that AB = AM + MB. But we were told that AM is congruent to CN and MB is congruent to ND. And so we have that AB = CN + ND. but CN and ND are the segments that compose CD. therefore, AB = CD
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  7. #7
    Junior Member Melancholy's Avatar
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    That's a good proof, Jhevon. Thank you. How do you get your mind to find it though lol?

    Also, is there any particular method I could use to help me study for a test on algebraic and paragraph proofs, postulates, theorems, truth tables, truth values, an etc? It's so stressful! I need to find a way to understand it all! ... because my teacher is unfortunately not teaching. He's preaches


    Could someone help me with this proof?

    Write a two column proof.

    Given: /1 and /2 are supplementary
    _____/3 and /4 are supplementary
    _____ / 1 [is congruent to] / 4

    Prove: / 2 [is congruent to] / 3

    So I start with my Statements and reasons chart...

    Statements___________________| Reasons
    1. /1 and /2 are supplementary.___ Given
    _ /3 and /4 are supplementary.
    _ /1 = /4

    2. m /1 + m /2 = 180____________Definition of Supplementary Angles
    _ m /3 + m /4 = 180

    3. m /1 + m /2 = m /3 + m /4_____Substitution

    4. m /1 = m /4_________________Definition of congruent angles

    5. m /2 = m /3_________________???

    6. /2 [is congruent to] /3________???
    I got this far... what are the last two?
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