Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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Flowchart proofs are organized with boxes and arrows; each "statement" is inside the box and each "reason" is underneath each box. Each statement in a proof allows another subsequent statement to be made. In **flowchart proofs**, this progression is shown through arrows. Flowchart proofs are useful because it allows the reader to see how each statement leads to the conclusion.

There are 3 main ways to organize a proof in Geometry.

The first way that isn't used that often is called the paragraph proof, the second way is called the two column proof and the third method is called flowchart proofs, so here its really easy to see using a picture your reasons and what your reasons allow you to conclude, so I'm going to show what a typical flowchart proof will look like when you're trying to say that 2 parts of corresponding triangles are congruent.

You're going to start off with 3 different boxes here and you're either going to be saying reasons that angle side angle so 2 triangles are congruent or it might be saying angle angle side or you might be saying side angle side or you could say side side side, so notice I have 3 arrows here. You're going to have 3 reasons no matter what that 2 triangles are going to be congruent, so in this box you're usually going to be saying triangle blank is equal to triangle blank and under here you're going to have one of your reasons angle side angle, angle angle side, side angle side or side side side so what goes underneath the box is your reason. Once you say that these two triangles are congruent then you're going to say that two angles are congruent or you're going to say that two sides are congruent and your reason under here is always going to be CPCTC, Corresponding Parts of Congruent Triangles are Congruent.

Now notice that I have a couple sometimes up here, sometimes you will be able to just jump in and say that 2 angles are congruent so you might need to provide some reasons. If I prompt tells you that 2 lines are parallel, then you might be able to say that alternate interior angles are congruent, so you might need to have some other reasons before you can get into angle side angle, angle angle side, side angle side or side side side. Other times if the proof is asking not just our two angles corresponding and congruent but they might ask you to prove that two triangles are isosceles so you might have another statement that this CPCTC allows you to say, so don't feel like this is a rigid one size fits all, because sometimes you might have to go further or you might have to back and say wait a minute I can't say this without previously having given this reason.