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Thread: Two Column Proof im so confused

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    Two Column Proof im so confused

    Two Column Proof im so confused-14731396_794857520655880_8171352330547881319_n.jpg
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    Re: Two Column Proof im so confused

    Quote Originally Posted by em19625 View Post
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    To start with, can you find a description of how to prove it? That is, how do you show that two triangles are congruent?

    -Dan
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    Re: Two Column Proof im so confused

    What are you confused about? It is impossible to give you any help or suggestions without knowing what you can do. You are given a rectangle, ACDE, with B the midpoint of side AC. Lines BD and BE are drawn. You are asked to prove that triangles BAD and BCE are congruent.

    Okay, what do you know about congruent triangles? Do you know "Side-Side-Side", "Side-Angle-Side", and "Angle-Side-Angle". Since any two right triangles have the right angles congruent, as well as having the third side determined by the other two, there are special congruence theorems for right angles.
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    Re: Two Column Proof im so confused

    im Confused on how to do the steps and then label the reasons
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    Re: Two Column Proof im so confused

    If you really mean that you have no idea what this is about, you need to talk to your teacher.
    Thanks from phys251
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    Re: Two Column Proof im so confused

    Hint ... Hypotenuse-Leg congruence of right triangles
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    Re: Two Column Proof im so confused

    Quote Originally Posted by em19625 View Post
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    Now I have a simple question: Are there many programs that still teach two-column proofs? I ask because I am of the impression that was abounded at least fifty years ago.
    Last edited by Plato; Oct 26th 2016 at 02:35 PM.
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    Re: Two Column Proof im so confused

    i have so far
    1.angle BED=angleBDE given
    2.Triangle BDE is isosceles angles BED and BDE are equal
    3.Side BE=Side BD triangle BDE is isosceles
    4.triangle EAB=triangle DCB triangles are congruent
    5.BA=BC, BE=BD each triangle is right angled
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    Re: Two Column Proof im so confused

    Quote Originally Posted by HallsofIvy View Post
    ...You are given a rectangle, ACDE...
    Actually ACDE is not mentioned to be a rectangle in the original problem. It can be proved that it is, though I wouldn't use that fact at the start of the proof. (I know you didn't, I'm just being fussy about the matter. )

    @Plato: I learned two column proofs when I was in HS about 25 years ago. Just for the record.

    -Dan
    Last edited by topsquark; Oct 26th 2016 at 03:34 PM.
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    Re: Two Column Proof im so confused

    Quote Originally Posted by em19625 View Post
    i have so far
    1.angle BED=angleBDE given
    2.Triangle BDE is isosceles angles BED and BDE are equal
    3.Side BE=Side BD triangle BDE is isosceles
    4.triangle EAB=triangle DCB triangles are congruent
    5.BA=BC, BE=BD each triangle is right angled
    You are fine up to 4. How do you conclude that the triangles are congruent? You need to be specific here.

    -Dan
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    Re: Two Column Proof im so confused

    what is wrong with number 5
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    Re: Two Column Proof im so confused

    Quote Originally Posted by em19625 View Post
    what is wrong with number 5
    There's nothing wrong with it. However it is not something you need to prove...it was a given statement and you need it to prove congruency with it so it's in the wrong place.

    -Dan
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    Re: Two Column Proof im so confused

    Quote Originally Posted by topsquark View Post
    Actually ACDE is not mentioned to be a rectangle in the original problem. It can be proved that it is, though I wouldn't use that fact at the start of the proof. (I know you didn't, I'm just being fussy about the matter. )

    @Plato: I learned two column proofs when I was in HS about 25 years ago. Just for the record.

    -Dan
    How do you prove that ACDE is a rectangle?
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    Re: Two Column Proof im so confused

    Quote Originally Posted by bjhopper View Post
    How do you prove that ACDE is a rectangle?
    That cannot be proved from the given.
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    Re: Two Column Proof im so confused

    Quote Originally Posted by Plato View Post
    That cannot be proved from the given.
    Actually it can. However it is not needed to solve the problem. (The proof is also a bit longer than I had thought.)

    Quickly speaking we can show that triangles EAB and DCB are congruent. Doing some angle work we can show that angles BED and ABE are equal. We now have two lines (AC and ED) cut by a transversal (BE) and alternate interior angles are the same so AD and ED are parallel. From here take AE to be a transversal cutting across two parallel lines (AC and ED again), where BAE is a right angle, and thus so is DEA. etc. So we have a 4 sided figure that has right angles on each corner. Thus ACDE is a rectangle.

    -Dan
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