1. ## 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.

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!

2. ## Re: Two column proof

Originally Posted by MathEd
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.
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.