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congruence of two triangles

Problem: In ΔABC, D is on segment *BC*, E is on *AC* and F is the intersection of segments *EB* and *AD*. Assume further that *AC* ≅ *BC* and *EC* ≅ *DC*. Prove ΔAFE ≅ ΔBFD.

The picture is given as an attachment.

Show △AFE≅△BFD

* Oh anything such as AC≅BC are line segments without the line notation on top of each pair of points. I couldn't figure it out with latex.

Partially completed proof

1. Assume AC≅BC amd EC≅DC. 1. Assumption

D is on segment *BC*, E is on *AC*

F is the intersection of segments *EB* and *AD*

2. http://whatis.techtarget.com/WhatIs/images/angl-sym.gifAFB ≅http://whatis.techtarget.com/WhatIs/images/angl-sym.gifDFB 2. Vertical angles

//http://whatis.techtarget.com/WhatIs/images/angl-sym.gifEFD ≅http://whatis.techtarget.com/WhatIs/images/angl-sym.gifAFB

3. AE is congruent to DB 3. derived from step 1

4. http://whatis.techtarget.com/WhatIs/images/angl-sym.gifCAB≅ http://whatis.techtarget.com/WhatIs/images/angl-sym.gifCBA 4. Lemma A- In △ABC if AC≅BC then the base angles are congruent

5. △ABC is an isosceles 5. Isosceles triangle theorem- A triangle is isosceles iff the base angles are congruent.

triangle

6.AB≅AB 6. Reflexive property

7. △ADB≅ △AEB. 7. SAS postulate

8.

I almost have everything but I just can't seem to figure these last steps. Somehow I don't know how to show point F where the two line segments EB and AD meet is the midpoint or something.

I got it. I concluded with ASA.

Re: congruence of two triangles

You have not completely stated the problem, just given a picture. What are you **given** about the lengths and angles here? You start with "1. Assume AC≅BC amd EC≅DC. 1. Assumption" Are you **given** that? Is that said in some part of the problem you haven't shown? If not, how can you simply "assume" it? If you are given it, then you should have said that here.

Re: congruence of two triangles

Oh ok Ive fixed that part. I put the entire question up.