SOLUTION: I have to write a two column proof. Here is a picture of the problem: https://docs.google.com/document/d/1a_S-POcquYF2qVL81mza1vSwA0iz77GdG5NcdxVvVmY/edit?usp=sharing

Algebra ->  Geometry-proofs -> SOLUTION: I have to write a two column proof. Here is a picture of the problem: https://docs.google.com/document/d/1a_S-POcquYF2qVL81mza1vSwA0iz77GdG5NcdxVvVmY/edit?usp=sharing      Log On


   

Question 1059721: I have to write a two column proof. Here is a picture of the problem: https://docs.google.com/document/d/1a_S-POcquYF2qVL81mza1vSwA0iz77GdG5NcdxVvVmY/edit?usp=sharing
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20066) About Me  (Show Source):
You can put this solution on YOUR website!
Given: AB ≅ AC
M is the midpoint of BC
Prove: AM bisects ∠BAC 


AB ≅ AC           |  Given
                  | 
ΔABC is isosceles | Definition of isosceles Δ
                  |
∠B ≅ ∠C          | Base ∠s of an isosceles Δ are ≅
                  | 
BM ≅ CM           | Given that M is the midpoint of BC 
                  | 
ΔABM ≅ ΔACM       | Side-angle-side 
                  |
∠BAM ≅ ∠CAM      | Corresponding parts of ≅ Δs.
                  |
AM bisects ∠BAC   | It's two parts are ≅.

Edwin

Answer by ikleyn(52925) About Me  (Show Source):
You can put this solution on YOUR website!
.
Ooo, how happy I was !

    In my youth years !

        When I studied Geometry !

            Written in lines !!

                and NOT in two columns !!!


Writing geometry proofs in two columns is invention of typography managers.
It has no any relation to Science.

    Euclid wrote everything in lines.

    More than 2000 years after Euclid the people wrote Geometry in lines.

    You will not find math proofs in math journals written in two colums.


Writing in two columns is the same as cutting the pages in the Geometry book with beautiful proofs by scissors along each page from the bottom to the top.

Is the same as cutting every thought in two pieces and placing peaces in two columns.

Is the same as jumping over a profundity in two jumps.

Absolutely nonsense activity.

    And even worst.

        Much worst.

The outcome of teaching geometry this way is/are the people/students who do not understand Geometry and Math and hate it.

And, in addition, can not formulate correctly any logically connected thought/point of view/conception.


                Sorry. My personal opinion.


Ooo, how happy I was ! (See again from the beginning . . . )


And by the way, see the normal/regular Geometry proof written in lines in the lesson
    - An altitude, a median and an angle bisector in the isosceles triangle
in this site.

Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.   It contains EVERYTHING you need to know, and everything is written in lines.

The referred lesson is the part of this online textbook under the topic "Triangle properties".