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Geometry Triangle Congruence - Should be easy?

  1. Feb 11, 2012 #1
    Geometry Triangle Congruence - **Edited to include diagram**

    1. The problem statement, all variables and given/known data

    Hi! The three simple geometry problems are in the attached photo. Sorry if they're difficult to read. I haven't seen this information in so long, and could use some help. :D

    Can you use the given information to determine that (AB) = (BC) ̅? Justify your answer.


    3. The attempt at a solution


    1. I would say that we cannot conclude AB = BC, because we have ***, which you can't conclude anything from.

    2. Yes, AB = BC, because we have two right triangles, BE = BE, and AE = EC. Thus the hypotenuses must be the same?

    3. I feel like the answer is yes here. Can one say that BD bisects angle ABC? Therefore, we have ASA?

    Thanks a lot guys/girls!
     

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    Last edited: Feb 11, 2012
  2. jcsd
  3. Feb 11, 2012 #2

    SammyS

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    Re: Geometry Triangle Congruence - **Edited to include diagram**

    You are correct. Answers are: no, yes, yes.

    For #1 you haven't given a reason.

    For # 3, how do you know the the angle is bisected? BTW: You could have used SAS immediately.
     
  4. Feb 11, 2012 #3
    Thanks Sammy!

    For #1, I apparently typed a banned word via the abbreviation for angle-side-side. Whoops!

    Is that a legitimate reason now to say no?

    Also, for #3, I see now that the angle bisection comment is irrelevant and not necessarily justified either. When can you say that an angle is bisected?

    Thanks again!
     
  5. Feb 11, 2012 #4

    SammyS

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    Yes, for #1 A$$ is as good as SSA .
     
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