GEOMETRY

[goalkeeper12]

HELP!!!

Okay here's the question...
Write a 2-column proof.
Given: AB=DC; AD=BC; AF=CE
Prove: segment DE is parallel to segment BF

(hint first prove triangle ABC is congruent to triangle CDA. use this fact to show angle 1 and angle 2 are congruent. then prove the other 2 triangles are congruent.)

Here's the picture: (I COULN'T MAKE A LINE FROM A TO C-SO THAT IS A DIAGONAL LINE AND THEN FROM B TO F- THERE IS A DIAGONAL LINE TOO...BOTH LINE AC AND LINE BF TOUCH EACH OTHER....INADDITION FROM D TO E THERE IS A LINE AND ALSO TOUCHES LINE AC)

      A ------------------- B
     /   1                 /
    /                     / 
   /                F    / 
  /           E         /
 /                     /
D ----------------2-- C

PLEASE HELP... THANK YOU!!!

 

[goalkeeper12]

HELP!!!

Okay here's the question...
Write a 2-column proof.
Given: AB=DC; AD=BC; AF=CE
Prove: segment DE is parallel to segment BF

(hint first prove triangle ABC is congruent to triangle CDA. use this fact to show angle 1 and angle 2 are congruent. then prove the other 2 triangles are congruent.)

Here's the picture: (I COULN'T MAKE A LINE FROM A TO C-SO THAT IS A DIAGONAL LINE AND THEN FROM B TO F- THERE IS A DIAGONAL LINE TOO...BOTH LINE AC AND LINE BF TOUCH EACH OTHER....INADDITION FROM D TO E THERE IS A LINE AND ALSO TOUCHES LINE AC)

      A ------------------- B
     /   1                 /
    /                     / 
   /                F    / 
  /           E         /
 /                     /
D ----------------2-- C

PLEASE HELP... THANK YOU!!!

 

[stapel]

I'm sorry, but I can't tell what you've added or changed in your second posting above. Please reply with clarification.

When you reply, please explain which angles are "1" and "2". Using letters (such as "angle DCE", etc) would be helpful. Also, you already have the diagonal AC, but you don't state how DE and BF relate to the other segments, other than that, if I understand you correctly, E and F lie on AC. But I'm pretty sure we'd need more information than that.

Thank you.

Eliz.

 

[soroban]

Hello, goalkeeper121

I think I decoded the description . . .

Given: AB = DC; AD = BC; AF = CE
Prove: segment DE is parallel to segment BF

              A                       B
              *-----------------------*
             /  * 1             *    /
            /     *       *         /
           /       F*              /
          /           *           /
         /              *E       /
        /         *       *     /
       /    *             2 *  /
      *-----------------------*
      D                       C

I'll give you the game plan . . . you can work out the details.

Since \(\displaystyle AB\,=\,CD\) and \(\displaystyle AD\,=\,BC,\:ABCD\) is a paralleogram.

So \(\displaystyle AB\,\parallel\,CD\) . . . and \(\displaystyle \angle 1\,=\,\angle 2\,\) (alt.int angles).

Since we also have: \(\displaystyle AB\,=\,CD\) and \(\displaystyle AF\,=\,CE:\;\Delta AFE \underline{\sim} \Delta CED\;\) (s.a.s)

Then: \(\displaystyle \,\angle AFB\,=\,\angle CED\;\) (corresponding parts)

Hence: \(\displaystyle \,\angle BFE\,=\,\angle DEF\;\) (supplements of equal angles)

Therefore: \(\displaystyle \,DE\,\parallel\,BF\;\) (alt-int. angles)

 

[goalkeeper12]

Thank you so much!!! All of you...I extremely appreciate it!!!

Thanks again!