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How To Do Proofs In Geometry?

Construct a two-column table. Label the left side “Statements” and the right side “Reasons.” Then list all given information in separate lines on the left. On the right of these write “given.” Then reflect on what you can conclude from the givens. For example, if you’re given an angle bisector, consider what that implies. In your statements column, you could indicate that two bisected angles are congruent and in the right column write “definition of an angle bisector.”

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Like the name suggests, a geometric proof is an attempt to prove a statement with logic. The first step in writing a proof is to construct a chart that has two columns. You should label the left column “statements” and the right column “reasons.”

The problem you are given will include a given statement as well as a statement that you have to prove. For example, let’s look at the following problem.

Given: Triangle EFG is an isosceles triangle, with base EG. Line FE is congruent to Line FG. Line FH bisects angle EFG.

Prove: Angle E is congruent to Angle G.

Your first statements in your statements column should repeat the given information. In this case, you would write that Line FE is congruent to Line FG. In the reasons section directly to the right, you will write the word “given.” Then your next line underneath the first one in the statements column will be “Line FH bisects angle EFG.” Again you will write “given” as your reason for this.

Now that you have established your givens, you need to think about the rules of the shapes you are working with to help your prove your point. For example, in this case you should consider why the problem told you that there is an angle bisector. Recall the definition of an angle bisector. This definition states that an angle bisector splits the angle into two equal parts. This means that Angle EFH and Angle GFH are congruent. Thus your third statement should be that these two angles are congruent and your reason should be “definition of an angle bisector. You should continue unpacking the given information until you reach a line where your statement is what the problem has asked you to prove.

For instance, in this example, you can use the reflective postulate to prove that FH is congruent to FH and then the Side Angle Side postulate to prove that Triangle EFH and Triangle GFH are congruent. From there you can prove that Angle E is congruent to Angle G with the reason “CPCTC” meaning that corresponsing parts of congruent triangles are congruent.