Geometry question please help :/

[Danielle7]

Hi,
I'm having a horrible time with one of my assignments. I just don't understand it at all and would greatly appreciate it if anyone was willing to help me.
my question is this:
Write a 2 column proof
Given: triangle AEB is congruent to DEC
angle ABC is congruent to angle DCB

Here is the diagram: http://i897.photobucket.com/albums/ac18 ... ometry.png

You may need to zoom in a bit. Thank you to anyone who will help I appreciate it so much you have no idea.

 

[Mrspi]

Hi,
I'm having a horrible time with one of my assignments. I just don't understand it at all and would greatly appreciate it if anyone was willing to help me.
my question is this:
Write a 2 column proof
Given: triangle AEB is congruent to DEC
angle ABC is congruent to angle DCB

Here is the diagram: http://i897.photobucket.com/albums/ac18 ... ometry.png

You may need to zoom in a bit. Thank you to anyone who will help I appreciate it so much you have no idea.

You are GIVEN that triangle AEB is congruent to triangle DEC. If two triangles are congruent, then each pair of corresponding sides must be congruent. In particular, AB is congruent to DC (I picked those because they are also parts of the triangles we WANT to prove congruent...triangle ABC and triangle DCB).

You are also GIVEN that angle ABC is congruent to angle DCB, which is nice because those are angles in the triangles we want to prove congruent.

So, at this point, we have triangles ABC and DCB with ONE pair of congruent sides and ONE pair of congruent angles....

LOOK at the diagram. It might help if you outline triangle ABC in one color, and triangle DCB in another color. Do you see that side BC is part of each of the triangles? BC must be congruent to BC, right? So that gives us a second pair of sides that are congruent, and the two triangles ABC and DCB must be congruent by the SAS congruence postulate.

I'll leave the part about "writing a two-column proof" up to you!

 

[soroban]

Hello, Danielle7!

There are enough facts for the proof.
Why are you having "a horrible time"?

$\displaystyle \text{Given: }\:\Delta AEB \cong \Delta DEC$

$\displaystyle \text{Prove: }\:\angle ABC \:=\:\angle DCB$

    A o                                       o D
       *  *                               *  *
        *     *                       *     *
         *        *               *        *
          *           *   E   *           *
           *              o              *
            *         *       *         *
             *    *               *    *
            B o   *   *   *   *   *   o C

\(\displaystyle \begin{array}{ccccccc}1. & \Delta AEB \cong \Delta DEC && 1. & \text{Given} \\ \\ 2. & AE = DE && 2. & \text{Corr. parts} \\ & AB = DC \\ & EB = EC \\ \\ 3. & AE + EC \:=\E + EB && 3. & \text{Add'n Prop.} \\ & AC =DB \\ \\ 4. & BC = BC && 4. & \text{Identity} \\ \\ 5. & \Delta ABC \cong \Delta DCB && 5. & s.s.s \\ \\ 6. & \therefore \; \angle ABC = \angle DCB && 6. & \text{Corr. parts} \end{array}\)

 

[Danielle7]

Well I'm having a horrible time because this is confusing to me. I'm sorry but not everyone understands things like this. Maybe it's easy for you but it's very confusing for me. Plus you and the other person who answered gave me two completely diff. answers. Now I'm more confused. :roll:
But thank you both for answering :mrgreen:

 

[Danielle7]

Both of you put different answers and now I'm more confused I wonder who is right :roll:

Thank you for answering though :mrgreen:

 

[tkhunny]

They are not "different" answers. The task is to prove. Proof doesn't much care how it is established. There are over 500 proofs of the "Pythagorean Theorem".