More about isosceles

Well, though there are still so many serious unsolved problems in the world, today I would like to write about geometry again.

When I had applied to take this lecture of geometry in the university, I had not known this was aimed to train the students to be a teacher of junior high school. When I knew it, I felt like a bit sorry “So we would only repeat mathematics for junior high school? It might be unnecessary for me, who doesn’t plan to be a teacher.”

But so soon as at the first day I could confirm myself, that I was right to take this lecture.
Although the question is for junior high school, the professor always shows us many important ideas that we had ignored.

We are still discussing how to prove the axiom “In an isosceles both base angles are same in measure”.

For this proof one should write:

“Let D to be the midpoint of the side BC”

D is the midpoint of the segment BC

Then I asked the professor: “Should we also write that Draw the segment AD to join A and D?”
He answered “You could write, but not needed. You can call it just as AD…because the segment is the only figure one could drawn when only two points are given as information.”

I asked him one more: “Can’t we describe the midpoint D as The point D for which BD=CD ? ”
He answered:
“Then you must write The point D on the side BC, or there might be another case of BD=CD for a point D”

Another case of BD=CD for a point D

“That might be complex, so it would be simpler just to use the name midpoint.”

Our discussion on an isosceles will be continued more.

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