Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

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)*

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,844

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

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

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)*

Offline

**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

Any????

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,030

What does equal mean in terms of geometric figures?

Here lies the reader who will never open this book. He is forever dead.

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.

Offline

**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

anonimnystefy wrote:

What does equal mean in terms of geometric figures?

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

Offline

**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

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)*

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,030

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?

Here lies the reader who will never open this book. He is forever dead.

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.

Offline

**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

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 ^^

Offline