4. It is too messy to prove some theorems in math.
THAT IS,
let's become to be able to prove your theories as correct by yourself.
When you want to say to other people
what you found in your brain,
not what you heard from someone,
what you can do?
If you said something wrong,
your words make the other person confused,
and you said a demagogy, that is, a false rumor,
then you have risks to lose your trust from other people.
If you are said by your friends,
"He always says something with light tongs,
but I found nothing correct in them,"
and you become to be believed by no one.
It is a big trouble for you, I think.
So, then,
you must show your theories have conclusions
which correctly follow by logic from facts or axioms or theorems
which are clearly shown correct,
and you must defense yourself by yourself.
To be understood by other people that your theories are correct,
we must have skills of proves.
Problems of proving something in math exists for those trainings for you.
So,let's reach your conclusions by logic with saying their roots neatly and clearly.
OH!
You, who feel messy to write "in ", such as "in a triangle ABC and a triangle DEF",
at your answers' top.
There are many and various topics of matters to say in this world.
If you do not inform what you will speak about in advance
and you speak only how it is,
no one can not understand and follow your talks.
For example,
if you only talk your friends how interesting it is,
but if your talking title is lacked
and your friends do not know what game title you are talking about,
you will only speak selfishly your words like utters.
Such situations make serious confusions
for building healthy friendships between both of you and your friends.
if you do not write words, "in ",
you will do very such as actions to your markers (I think, your teachers)
on a large scale in your test papers.
An attitude, "because you are (I do not know following words),
you can understand what I want to say without words,"
are never understood by complete strangers.
So I recommend you to get into the habit that
you clarify what you are going to talk about.
Do not omit needed words to be understood yourself by other people.
(For example, at small stores, you operate a cash register.
Many your customers are completely strangers.)
You must show your rightness to other people by your words and your proofs.
In such situations, proof skills will be very helpful for you.
Let's training proof skills by problems in math
which make simpler than real world's problems.
", such as "in a triangle ABC and a triangle DEF",