Geometry proofs5/4/2023 ![]() This interprets the hypothesis of the theorem in terms of your drawing. Sometimes you have to translate the statement of the theorem into the specifics of your drawing. This represents the hypothesis of the theorem. You will prove that AOB = DOC.Ī formal proof has a definite style and format consisting of five essential elements. In your picture, the vertical angles are AOB and DOC. The general conclusion is that vertical angles are congruent. The next step is to interpret what you would like to prove in terms of your picture. In mathematical terms, you write that AC intersects BD at O. In your picture, the two intersecting lines are AC and BD. For the vertical angle example, you are given two lines that intersect. Your diagram doesn't need to be set in stone until the proof is done.Īfter you've drawn your picture and labeled the important points, segments, lines, and so on, you have to interpret the hypotheses in terms of your picture. You can always add labels to your pictures. Sometimes as you work through a problem you realize that you need to label more things. It's helpful to have your picture as complete as possible before beginning your proof, but that's not always possible. Try and include all of your assumptions in your picture. Your mission is to show that these two angles are congruent.īy drawing a picture, you've translated the general statement of the theorem into a specific example that you can pick apart and analyze. They form a couple of vertical angles, which you've named AOB and DOC. Here you have two intersecting lines, AC and BD. You can translate your general statement into the picture in Figure 8.1. When you draw a picture illustrating what's going on, it's easier to see what you are assuming and what you are trying to prove. That's why in geometry a picture is worth a thousand words. Because everything is so general, it's hard to get a handle on where to start. The statement does not even name the vertical angles formed. This statement is vague in that it does not name the specific lines that intersect or give the point of intersection. For example, you have already learned that when two lines intersect, the vertical angles formed are congruent. ![]() The hypotheses and conclusion are usually stated in general terms. ![]()
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