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## Topic review (newest first)

ShivamS
2013-03-26 02:42:56

Glad to see that we both were clarified.

bob bundy
2013-03-26 01:43:07

You're welcome.  I have learnt something too.

Bob

ShivamS
2013-03-26 01:41:48

Yes, so it is congruent because it coincides. Thank-you both.

bob bundy
2013-03-26 01:33:49

Thanks.  And that uses SAS (axiomatic) to prove the others.  Hhhhmm!

http://www.proofwiki.org/wiki/Triangle_ … e_Equality

Bob

ShivamS
2013-03-26 01:12:18

Check this out.
http://www.math.washington.edu/~king/coursedir/m444a03/notes/congruence%20html/tri-congruence-summ.html
That includes proof for the congruence criterias.

bob bundy
2013-03-26 01:09:12

Prove 'perpendicular'.

Sorry, I'm not being awkward just to be nasty.  I really have never seen any proofs for this sort of thing.  I think congruency appears very early in Euclid (trying to check this now) and properties of kites much later.  So I'm worried that this proof leads to a circular argument.  I'll try to find out.

Bob

ShivamS
2013-03-26 00:58:40

Well if we have a perpendicular bisector as the diagonal, then by SAS we can see that they are congruent.

bob bundy
2013-03-26 00:56:37

#### Shivamcoder3013 wrote:

.... they make a kite................. That proves that the triangles are congruent.

Why does it prove that?

The kite has the right properties but are you sure that those properties don't depend on congruency (circular argument).

Bob

ShivamS
2013-03-26 00:54:48

Oh okay then. So because the sides and angles coincide (ABC and DEF) making them congruent, that would be a valid proof for Side-Angle-Side? Anyways, thank-you both.

bob bundy
2013-03-26 00:52:46

thanks Stefy

Followed the link to

http://www.proofwiki.org/wiki/Triangle_ … e_Equality

Is that enough?

Bob

ShivamS
2013-03-26 00:51:41

For example, to prove Side-Side-Side, using Side-Angle-Side, we just make two triangles such that they make a kite (being diagonal). That proves that the triangles are congruent.

bob bundy
2013-03-26 00:47:35

My difficulty is I have never seen any proved so I'm not sure where to start.  That's why I need to see one that you have already done.  Then I can see what you are after.

Let me be specific.  The diagram below has two triangles.

Corresponding sides are equal as shown.  So what can you prove from this?

Bob

anonimnystefy
2013-03-26 00:46:01

I have found this: http://www.proofwiki.org/wiki/Triangle_ … ity#Part_1.

Seeing how it has been two years since I have done axiomatic geometry, I do not remember what can and what cannot be used in the proof...

bob bundy
2013-03-26 00:39:32

My difficulty is I have never seen any proved so I'm not sure where to start.  That's why I need to see one that you have already done.  Then I can see what you are after.

Bob

ShivamS
2013-03-26 00:30:53

Well isn't SAS just an axiom? How do you prove that: If 2 sides and angles in a triangle are congruent to two sides and angles of another triangle, the triangles are congruent. Like take 2 triangles: ABC, DEF. If AB=DE, AC=DF and angle A = angle D, the triangles ABC and DEF are congruent.