Deductive reasoning is the process of reasoning logically from given statements to make a conclusion. Deductive reasoning is the type of reasoning used when making a Geometric proof, when attorneys present a case, or any time you try and convince someone using facts and arguments.
There are two types of reasoning that we use in Geometry, inductive reasoning and deductive reasoning and often we like to compare the two. Deductive reasoning is the process of reasoning logically from given statements to a conclusion. So let's say you wanted to have a later curfew. To justify it to your parents, you're going to have to use deductive reasoning and say something to along the lines of "I'm a responsible person, I get good grades, I've been able to honor every other curfew." So basically, you need to back yourself up to make your statement that you think that you need a later curfew. To give you little more idea of what is deductive reasoning compared to inductive reasoning, let's say I ask you to prove that this quadrilateral qu ad is a parallelogram and I told you that qd is parallel to ua and that qu is parallel to da. So if I just mark these that qd parallel to ua and that qu is parallel to ad. This process of which you would use of proof that is called deductive reasoning because you're using given information to make a proven statement. Now to compare this with inductive reasoning, let's say I gave you these three shapes and I said "draw the next shape in the sequence." Well, you're going to see that we have an equilateral triangle an equilateral quadrilateral and an equilateral pentagon. So you're going to observe the pattern that all of these shapes are going up in one number of side and that the sides are all congruent. It's an equilateral figure. So you know that the next shape in the sequence will be an equilateral hexagon. There you didn't have a given statement, you didn't prove anything, you just saw the pattern and you reached the conclusion of what the next shape would be. So this, would be inductive reasoning. If you're ever given a quiz question where it says "is this inductive or deductive reasoning?" Ask yourself, are you being asked to prove or show something and justify it or are you just observing something and making conclusion based on patterns that you see. And that will tell you if it is inductive or deductive reasoning.