Triangle Perimeters and congruency

[MattB]

the question:
If two triangles have equal perimeters, then they have congruent sides.

Is this true or false? If false, i have to draw/show a counter example. If true, all i have to show is what is given and what needs to be proved; no proof to be done.

[stapel]

Just think about it: Take a loop of string (or a rubber band, whatever). Its perimeter (length) is fixed (as long as you don't stretch the rubber band). Now use three fingers to pull it out into a triangle. Is there only one triangle you can form?

Eliz.

[MattB]

Thanks! Now i feel really stupid :)

Intuitively i knew it was false, but couldn't grasp the common sense :)

[stapel]

Don't be afraid to put things in really practical, even mundane, terms when you can. Mind experiments can be very useful. A picture isn't a proof, but it can go a long way toward helping you figure out the truth-value of a statement, or how to approach the proof.

Glad I could help a little. :wink: :D

Eliz.