Help in simple proofs in geometry!!!?

Question

In the reason section of the 2 column proof, how will I know if I'm going to use a theorem or a definition?

Ex. Theorem of perpendicular angles or Definition of perpendicular angles?!!!

Answer 1

Example:

Problem: two guys start at the same spot and walk in opposite directions, each for 3 miles. Then they make a left turn and walk for 4 miles each and stop. How far are they apart?

Solution when they make a left turn then by definition they travel a right angles to their original path. By the pythagorean theorem we can now compute how far they are apart. From the startng point each one is sqrt(3^2 +4^2) = sqrt(25) = 5miles. So they are a total of 10 miles apart. Actually that's not a complete proof but you get the idea.
When you are solving a problem and you go from one step to another in your proof, sometimes the reason for the step is that you are transforming the problem into a form that is easier to solve. Sometimes the problem is presented in such away that you need to use formal definitions which then allow you to employ known properties and theorems relating the things that thave been formally defined. So you might have

Step 1 by definition
Step 2 by axiom
Step 3 by corollary
step 4 by definition
step 5 by theorem 1
step 6 by theorem 2
step 7 proof!

You'll get better with practice.

Answer 2

Ask yourself, in your own words, why each step follows from the last.

If the statement is that two angles are right angles after you've just stated that the lines are perpendicular, you could say "Definition of perpendicular lines" or you could say "Perpendicular lines intersect at right angles." Either would be acceptable. The purpose of a proof is to show a logical sequence of justified steps leading to a conclusion.

Answer 3

It depends. If the statement part follows from a definition, then you need the definition. If the statement follows from a theorem, then you need a theorem.

Answer 4

Simple Geometry Proofs