One of the biggest ideas in high school geometry is getting students to write a two column proof. Although proofs seem to be emphasized less these days, it is still an important concept to get across to students. Step by step logical argument is an important skill that can be applied to any career or aspect of life.
I like to start teaching proofs with something the students can relate to. I ask one student to come to the front of the room. I ask him or her to take of their shoe {must be a tie shoe!}. I then ask for a volunteer to give that student verbal directions on how to tie his or her shoe. I tell the demonstrating student that they must do exactly what the directions say. I use this exchange so students will hopefully see how important it is to be very specific and step-by-step with their directions.
Next, I like to use a couple of puzzles to continue to develop the idea that a step by step process is necessary when writing a proof. I use word puzzles that are sometimes called word ladders.
We then move on to another thing that students are very familiar with - solving algebra equations. I setup several algebra equations in two column form. Students get familiar with the format of a proof and start to understand how to move step by step through the process.
Finally, I feel that my students are ready for the big event...writing an actual geometry proof. Unfortunately, this sometimes doesn't live up to what I might have built it up to be.
As we move through the properties and apply them to geometric situations instead of algebraic ones, students start to get the idea.
Soon, we make it to congruent triangle proofs where these ideas are really applied. Introducing the ideas of congruent triangles slowly with MANY examples helps students get the idea. Using lots of different activities {task cards, board work, fill in the blank, etc}
I just finished making a flip book that I am going to use this year to introduce Congruent Triangle Proofs with CPCTC. One example on each page that students can fill in as we go. When we are finished, they can store it in their notebook by gluing down the back page if they wish.
Below are some links to products that you can use to help your students work on writing proofs in geometry.
Good luck!