#1

Is it possible to have 2 non-congruent triangles with the same area and perimeter? I heard something about using some theorem to solve it, but I'm not sure.

Answers? Thoughts?

Answers? Thoughts?

#2

Yes. Congruent means the angles of the two triangles are the same. They could easily have the same area and perimeter, I believe, though the case is rare. (First post back from being banned!)

#3

But its NOT congruent. Thats the kicker.

#4

I know. I said yes, that the triangles could still have the same area and perimeter. For example, if you take one cm from side one, and add that same cm to side two, you get a different triangle than triangle a, but triangle b has the same area and perimeter.

#5

So kind of like a triangle with side lengths 5,12,13. All you would do, for instance, was move 5 to where 12 would be, and you would have a different Triangle?

#6

So kind of like a triangle with side lengths 5,12,13. All you would do, for instance, was move 5 to where 12 would be, and you would have a different Triangle?

Nooo. That's just a different orientation.

#7

I believe the area might change if you changed a cm of side.

and no, he meant 1cm, not the whole side

and no, he meant 1cm, not the whole side

#8

I know. I said yes, that the triangles could still have the same area and perimeter. For example, if you take one cm from side one, and add that same cm to side two, you get a different triangle than triangle a, but triangle b has the same area and perimeter.

Thats wrong.

So your saying that say if I have a triangle of sides 4, 6, 8,

I should take one cm from one side and add it to another. So I can take one cm from the 8 side, and add it to the 4 side, to get a triangle of

5,6,7?

Triangle 4,6,8 = area 11.618...(approx)

Triangle 5,6,7 = area 14.696...(approx)

#9

probably something to do with the "a squared + b squared = c squared" theorem. i cant remember the damn name now. a, b, and c are the sides of the triangle, just so ya know.

#10

Simply put, yes, two non congruent triangles can have the same area and perimeter.

#11

^ ^ thats the pythagore theorem and only works on one triangle with a 90 degree angle, not two

#12

http://www.informaworld.com/smpp/content~content=a713816576~db=all

'...proves the following theorem: given any non-equilateral triangle, there exist infinitely many mutually non-congruent triangles with the same area and the same perimeter as the given triangle."

Therefore, it is possible

/thread

'...proves the following theorem: given any non-equilateral triangle, there exist infinitely many mutually non-congruent triangles with the same area and the same perimeter as the given triangle."

Therefore, it is possible

/thread

#13

then i would say possible

#14

Thats wrong.

So your saying that say if I have a triangle of sides 4, 6, 8,

I should take one cm from one side and add it to another. So I can take one cm from the 8 side, and add it to the 4 side, to get a triangle of

5,6,7?

Triangle 4,6,8 = area 11.618...(approx)

Triangle 5,6,7 = area 14.696...(approx)

Ahh, my bad, I was only figuring it for perimeter.

#15

Yeah, I just went through some serious calculus equations, and pumped out an answer. It involves some eclipsing and other retarded stuff, but yes, you just have to solve the triangle by using its original perimeter, or area, and then contorting different sides so that they end of the same side lengths/bases.

#16

http://www.btinternet.com/~se16/hgb/triangleareaperimeter.htm

#17

Yeah I think it's possible.

Triangle ABC is congruent to Triangle DEF.

But ABC is not congruent to Triangle FED, since that is saying that side AB=FE and BC=ED.

At least that's how congruence works in my geometry class. I don't know if order (of the letters) matters in other classes though.

Triangle ABC is congruent to Triangle DEF.

But ABC is not congruent to Triangle FED, since that is saying that side AB=FE and BC=ED.

At least that's how congruence works in my geometry class. I don't know if order (of the letters) matters in other classes though.