Difference Between Congruence and Equal (1 Viewer)

[frog1944]

Hi,

I've heard that equal is used for numbers, and congruence is to relate to "equal" shapes (same side lengths, same area etc.) in geometry but with a different location in space.

But I don't understand why we use congruences in algebra such as: 3x^2 + 9x - 2 (congruent to) A(x-2) + B(x-2)^2 + C

Could someone please explain this to me.

Thanks,

P.S I'm sorry for the lack of latex, I'm not sure how to insert it in this forum.

 

[leehuan]

Hi,

I've heard that equal is used for numbers, and congruence is to relate to "equal" shapes (same side lengths, same area etc.) in geometry but with a different location in space.

But I don't understand why we use congruences in algebra such as: 3x^2 + 9x - 2 (congruent to) A(x-2) + B(x-2)^2 + C

Could someone please explain this to me.

Thanks,

P.S I'm sorry for the lack of latex, I'm not sure how to insert it in this forum.

Congruence means that it's true for ALL x. It means "identity".

If we want to be pedantic, the trigonometric identities should all be written with a congruent sign, not an equal sign. (Of course it doesn't actually matter).


We basically want to find values for A, B and C so that the LHS is actually the exact same as the RHS ALWAYS.

 

[Green Yoda]

It's not congruency it means equivalent in this case.

 

[frog1944]

Ok, if I had y = 3x^2 + 9, should it be congruent or equal?

 

[Green Yoda]

Ok, if I had y = 3x^2 + 9, should it be congruent or equal?

Equal because they are intersecting. The other one we use 3 horizontal lines for 2 or more expressions to be equivalent. Congrugency is not the right word.

 

[InteGrand]

Ok, if I had y = 3x^2 + 9, should it be congruent or equal?

It should be equals. I don't think you lose marks in the HSC if you just always use the equals sign for identities or equations.

 

[frog1944]

Ok, in this question (http://community.boredofstudies.org/showthread.php?s=&goto=lastpost&threadid=352722) InteGrand you used congruent for part b, let w congruent to r^2 - z^2. Why did you use congruent instead of equal to?

 

[InteGrand]

Ok, in this question (http://community.boredofstudies.org/showthread.php?s=&goto=lastpost&threadid=352722) InteGrand you used congruent for part b, let w congruent to r^2 - z^2. Why did you use congruent instead of equal to?

I just did that because I was saying it was defined to be r^2 – z^2 (sometimes the triple bar is used when you're defining something equal). You don't really "need" to do it though, you can just use the equals sign if you want, and you certainly wouldn't lose marks if you did.

 

[frog1944]

Ok, thank you. I believe I understand it better. So only use congruent symbol in geometry (stating shapes are "equal" but not in position), for identities and for defining variables in terms of variables?

 

[InteGrand]

I guess so. If you're in doubt, just use the equals sign, since the HSC doesn't really care if you just use equals (whereas some markers may find it strange if you use triple bars in a place where it'd be better to use equals).

(Of course for geometry, use triple bars, not equals, for congruent shapes.)

 

[frog1944]

Ok, thank you very much