Help with Proof?

Question

2. Given: triangle ADF is congruent to triangle BEF Segment DC is congruent to segment EC
Prove: Triangle AEC is congruent to triangle BDC
Please iclude given statements in two colmun proof

Answer 1

The conclusion does not follow from the premises. Here's a counterexample:

A=(1, 2)
B=(2, -1)
C=(5/2, -3/2)
D=(4, 1)
E=(1, -4)
F=(0, 0)


We see that:

AD=√10
DF=√17
FA=√5

BE=√10
EF=√17
FB=√5

So by SSS, triangles ADF and BEF are congruent, as required. Further:

DC=√(17/2)
EC=√(17/2)

So DC is congruent to EC. Thus these points fulfill both of the given stipulations. However:

AE=6
BD=√8

So AEC is NOT congruent to BDC, because one of the corresponding sides are not congruent. Since the conclusion does not actually follow from the given premises, it is obviously impossible to prove it. This is one of those cases where either you have written the problem incorrectly, or your teacher is trying to mess with your head by giving you an impossible problem.

Answer 2

This not easy without a picture. I am tired, so can't try too hard. Here is a start: DC and EC give you 1/3 of it, and you need to work around that.

Answer 3

This seems kinda hard without being able to see the triangles. Maybe i'm wrong though.

Answer 4

OK

BUT there needs to be more information (like a diagram or a more complete description)