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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

Show that if a geometric figure is congruent to another geometric figure, which is in its turn congruent to a third geomtric figure, then the first geometric figure is congruent to the third.

We have the 3 geometric figures : A,B,C

With the information given: A congruent to B, B congruent to C

So, inversely, we will have :

B congruent to A, because A is congruent to B, so, its inverse must necessarely also be true, because if it wasn't we would a contradiction with the information given to us that A congruent B, but we know that it isn't the case, so the only option left is B is really congruent to A

C congruent to B

For the same reason has the above statement.

So, we have 3 geomtric figures congruent, because A is congruent to B, and having proved the inverse of B congruent C, that is, C congruent to B, we see that the two geometric figures(A and C) are also congruent to the same figure (B), and that...

A is congruent to C

*Last edited by Al-Allo (2013-08-23 11:49:14)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,664

hi Al-Allo

This seems to be a good way to prove this, but your proof is difficult for me to follow because I'm not clear which lines are in which shape.

Bob

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

We have the 3 geometric figures : A,B,C

With the information given: A congruent to B, B congruent to C

So, inversely, we will have :

B congruent to A, because A is congruent to B, so, its inverse must necessarely also be true, because if it wasn't we would a contradiction with the information given to us that A congruent B, but we know that it isn't the case, so the only option left is B is really congruent to A

C congruent to B

For the same reason has the above statement.

So, we have 3 geomtric figures congruent, because A is congruent to B, and having proved the inverse of B congruent C, that is, C congruent to B, we see that the two geometric figures are also congruent to the same figure (B), and that...

A is congruent to C

*Last edited by Al-Allo (2013-08-23 11:46:49)*

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

Any????

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

What does equal mean in terms of geometric figures?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

anonimnystefy wrote:

What does equal mean in terms of geometric figures?

Well, sorry for my mistake in terms, I meant congruent,xD

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

Ok, here's another version :

We have the 3 geometric figures : A,B,C

With the information given: A congruent to B, B congruent to C

So, inversely, we will have :

B congruent to A, because A is congruent to B, so, its inverse must necessarely also be true, because if it wasn't we would a contradiction with the information given to us that A congruent B, but we know that it isn't the case, so the only option left is B is really congruent to A

C congruent to B

For the same reason has the above statement.

So, we have 3 geomtric figures congruent, because A is congruent to B, and having proved the inverse of B congruent C, that is, C congruent to B, we see that the two geometric figures(A and C) are also congruent to the same figure (B), and that...

A is congruent to C

*Last edited by Al-Allo (2013-08-23 11:49:34)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

So, A is congruent to C because A and C are both congruent to B? Isn't that what you need to prove in the first place?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

anonimnystefy wrote:

So, A is congruent to C because A and C are both congruent to B? Isn't that what you need to prove in the first place?

Well, isn't it self evident?

Anyway, I think I should yes ^^

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