Help with Proofs

Question

Is there a specific way or order I can follow when needing to write a proof? Here’s my problem: I don’t know where to start with them. For example, if I knew the answer to a proof, I understand why the answer is the answer, but I would never have figured it out on my own.

Answer 1

Start simple! It takes practice. Look at examples, then apply the same kind of logic to other proofs.

Try this one:

If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

Start with a 3 digit number.

N = 100 H + 10 T + U

By hypothesis the sum of the digits is divisible by 3, i.e. H + T + U is divisible by 3. You need to get that sum out of your expression for N.

N =99 H + 9 T +( H + T + U)

Since H + T + U is divisible by 3 and the other 2 parts of the sum are divisible by 3, the whole number N must be divisible by 3.

In geometry it works the same way. Look first at the proof of "Pons Asinorum", the base angles of an isosceles triangle are equal. You must already know that 2 triangles are congruent when SAS = SAS. You must prove that 2 sets of triangles are congruent...follow the proof in your text book. Then apply the same kind of logic to prove that 2 triangles are congruent by SSS.

You cannot learn to prove theorems until you have looked at a few already done and then you learn by experience how to prove new things. Good luck.

BTW if you have specific examples, I can help you work through them without showing you the whole thing. I will show you the way to get to the answer. Just send me a message.