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Thread: Two column proof

  1. #1
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    Two column proof

    Hello,

    I'm currently teaching grade 8 kids how to do a two column proof.

    The topics revolve around the Properties of Equality, Segment addition postulate, angle addition postulate, definition of midpoint and angle bisector.

    A lot of things going in there. Is there any way to make the topic easier? let me attach a sample problem.

    Two column proof-.png C, N, H, S, T are all points inside angle PKT, angle PKN is congruent to angle HKT, angle PKC is congruent to angle SKT.
    Prove : angle CKN is congruent to angle HKS.


    It looks easy and it is, but students are having a hard time making connections and its also driving me nuts. I have already ran out ideas... HELP!
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  2. #2
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    Re: Two column proof

    Quote Originally Posted by MathEd View Post
    I'm currently teaching grade 8 kids how to do a two column proof.
    The topics revolve around the Properties of Equality, Segment addition postulate, angle addition postulate, definition of midpoint and angle bisector.++7
    A lot of things going in there. Is there any way to make the topic easier? let me attach a sample problem.
    Click image for larger version. 

Name:	??.PNG 
Views:	1 
Size:	11.5 KB 
ID:	37895 C, N, H, S, T are all points inside angle PKT, angle PKN is congruent to angle HKT, angle PKC is congruent to angle SKT. Prove : angle CKN is congruent to angle HKS.
    I am greatly surprised to see that anyone still uses a two column proof. A well written paragraph form has been standard for years. Moreover, the statement that $N$ interior to $\angle PKT$ means that $N$ is on the $T-$side of $\overleftrightarrow {KP}$ and on $P-$side of $\overleftrightarrow {KT}$.
    Now from the given.
    $ \begin{align*} m\left( {\angle PKN} \right) &= m\left( {\angle HKT} \right)\\\\m\left( {\angle PKN} \right) &= m\left( {\angle NKC} \right)+ m\left( {\angle PKC} \right)\\m\left( {\angle HKT} \right) &= m\left( {\angle HKS} \right)+ m\left( {\angle SKT} \right)\end{align*}$

    That it is.
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  3. #3
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    Re: Two column proof

    Two column proof-1.png
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