Learn about Geometric Proofs In this lesson, let's learn about geometric proofs. Geometric proofs are essentially proofs that we write using deductive reasoning. The way we do that is we usually have a two-column proof method. On the left column, we write the statements that make up the step-by-step how did we get from whatever is given to us to what we need to prove. On the right of the column, we write the reasons that make these statements a reality or true. So for example, in this particular case, what we’re given is angle one and two from a linear pair. So what I'm going to do is write down A, B, C and D. This is angle one, this is angle two. So we’re given that angle one and two from a linear pair and we have to prove that they are supplementary. So here is how we would do it. Right here arte the steps given to us. We are given three missing places we need to write how we got to these. So we start with angle one and two from a linear pair that’s given to us. If they form a linear pair, then, lines BC and AB must form a straight line. That’s the definition of a linear pair and we can see that’s true. If this is indeed the case, then the nest step that we infer from this, the deductive reasoning. The next step says; then the measure of angle A, B, C, this entire angle is 180 degrees. That’s the definition of a straight angle. That’s the reason why we can jump from this conclusion to this conclusion. If this is true, what's the next step for us? What we do, the hint given us is additive postulate. What this means is angle addition postulate says that the measure of angle one plus measure of angle two equals measure of angle A, B, C. Notice that this is angle one, this is angle two. The sum of these two is the measure of angle A, B, and C. How do I get that, from the angle addition postulate. So that’s the first missing blank. Then if this is true, we need to substitute steps three and four, is the reason given to us? That’s this. So instead of measure of A, B, C, I can substitute 180 degrees which means missing blank B is measure of angle one plus measure of angle two equals 180 degrees because if angle one and two, the sum of their measures equals the measure of angle A, B, C and we know from the previous step that measure of angle A, B, C is 180. Then these two are equal that’s the angle addition postulate and then next step is substituting measure of A, B, C with 180 degrees because that’s the substitution property of equation. Now that this is done, what do I know? Measure of angle one and two, they’re 180 degrees. Then, they are supplementary because this is the definition of supplementary angles. The definition of supplementary angles says they are supplementary if the sum equals 180 degrees. So notice what we did is we filled in the three missing pieces based on deductive reasoning.