# congruence of two triangles

• Feb 1st 2013, 06:47 AM
bonfire09
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 ACBC and ECDC. 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. A
ssume AC≅BC amd EC≅DC. 1. Assumption
D is on segment BC, E is on AC
F is the intersection of segments

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.

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.
• Feb 1st 2013, 07:03 AM
HallsofIvy
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.
• Feb 1st 2013, 07:06 AM
bonfire09
Re: congruence of two triangles
Oh ok Ive fixed that part. I put the entire question up.