What are some terms that you use in your everyday life that are really hard to define, yet they're incredibly important and frequently used? how could you explain why undefined terms become so important when we start to write proofs in geometry?

Step-by-step explanation:

Tough question.

Spiritual.

Love (if ever there was a misused word, it is love). I used to ask my classes what this sentence means "I love hunting." Try that one on. I don't know if you are dating someone, but how can you say "I love you." and "I love hunting." and not have something terribly wrong with the definition of the verb. One implies treasuring someone. The other means outfoxing a fox and murder.

Religion. Why are there so many different ones? The claim that there is only one true one makes the definition elusive to say the least. And it has caused a great deal of trouble.

Geometry: You have to know what a line segment is before you can say that one segment bears a relationship to another one.

You have to be able to define a point before you can calculate an intersection point of 2 lines or 2 curves or more.

You have to be able to define almost any term in geometry so that you can restrict enough to make it useful.

step-by-step explanation:

b and c

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this