Answer:
Some sites help you, but let me break it down for you. I will do more.
Hold on.
Step-by-step explanation:
https://study.com/academy/lesson/two-column-proof-in-geometry-definition-examples.html
A proof is a logical argument presented with factual statements in order to arrive at a conclusion. Writing a proof is like solving a puzzle or using Legos to create a model of something. Everything needs to fit in an appropriate place.
There are 3 main types of proofs:
a) Paragraph proof
b) Two-column proof
c) A flow chart proof
The two-column proof is the method we use to present a logical argument using a table with two columns and is the focus of this lesson.
For our discussion, we will use this following example:
Lisa forgot to punch her time card at work. She needs to prove to her boss that she got to work on time. She has a train ticket to show the time she took the train to work, and she has a Dunkin' Donuts receipt. She writes her boss the following email:
Dear Boss,
I have attached a copy of the train receipt showing the time I got on the train this morning. I also include another receipt to show that I bought donuts that are in the staff lounge and to show the time I bought the donuts. Henry, who is always on time, admitted that the donuts were in the staff room when he arrived. Had I punched in, he would have punched in after me. Therefore, based on the time Henry punched in, you can verify that I got to work on time.
Sincerely, Lisa
P.S. I'm glad to know that you enjoyed your favorite coconut sprinkled donut.
Lisa's explanation is an example of a paragraph proof, but let's look at her reasoning using a two-column proof.
Two Column Proof
Elements of a Two-Column Proof
There are 4 important elements to notice about two-column proofs.
1) The first column is used to write math statements.
2) The second column is used to write the reasons you make those statements.
3) The statements are numbered and follow a logical order.
4) You must end with the concept you are trying to prove.
In order to write any proof, we need certain items:
a) Givens: A mathematical proof always begin with the givens. Usually, we are given some details to build your proof. In Lisa's case, she had two receipts. Those are her givens. They already exist.
b) Diagram: If a diagram is not provided, draw a diagram based on the givens. A visual representation is very helpful before you start a proof.
c) Prior knowledge to connect statements: We must have prior knowledge of theorems, postulates, angle relationships, definitions, and other pertinent information, in order to build on your givens. Lisa knew that Henry is always on time. He had eaten a donut, and he punched in. This fact had nothing to do with her train ticket, but the donuts and Henry were connected to the donuts receipt.
d) Reasoning skills and patience: Writing proofs demands patience and time. Using necessary reasoning skills, we have to work through the ideas to ensure that they make sense.
e) Order: It is very important to show that the argument follows a certain logic and order. For example, first, Lisa started with the train ticket, which evidenced her journey to work that day. After the train, she stopped at Dunkin' Donuts. Next, she took the donuts to the office. Lastly, Henry had a donut. Henry was on time; therefore, we can reach the conclusion that Lisa was on time because the donuts got there before Henry.
