Things that are equal to the same thing are also equal to one another (Transitive property of equality).
If equals are added to equals, then the wholes are equal (Addition property of equality).
If equals are subtracted from equals, then the remainders are equal (Subtraction property of equality).
Things that coincide with one another are equal to one another (Reflexive Property).
The whole is greater than the part. Mathematical proofs is an argument, a justification, which convinces other people that something is true. Math isn’t a court of law, so a “preponderance of the evidence” or “beyond any reasonable doubt” isn’t good enough. Geometry teaches students like myself how to think critically and prove things in many ways using a step by step process. And if we didn’t use logics and reasonings then we would be jumping to conclusions and making up things a principle posited in the fourteenth century (by William of Occam (1288 C.E.–1348 C.E.)) includes that your proof system should have the smallest possible set of axioms and logical rules. Proofs are important to math since they allow us to think the way we do, analysis the reasonings for things logically.It's also, in real life since everything you do you have to have a reason and logic.