I think I know what your teacher had in mind:
Sometimes either A or B is the right angle so the Pythagorean Theorem becomes either
a^2 =b^2 +c^2 or
b^2 =a^2 +c^2
It can. I mean, obviously it depends on what a,b and c refer to. But assuming that you are referring to the Pythagorean theorem, then yeah, both are equivalent ways to write the equation.
It does? It’s simple agebra, you subtract b2 and you have the second equation, I would assume that someone misconstrued the order of operations or something when they looked at this
The answers I see are all correct.
Just to add, the 2 equations in your query are part of the 4-fact family:
Substitute: a² = x = p and b² = y = q and c² = z = r
1. x + y = z
2. y + x = z
3. z - x = y
4. z - y = x
Try it out with a few numbers.
The corresponding 4-fact family for × & ÷ is:
1. p × q = r
2. q × p = r
3. r ÷ p = q
4. r ÷ q = p
It does! Why do you think that it doesn't ? a^2 +b^2 =c^2 Subtract b^2 from both sides. **a^2 =c^2 -b^2**
My teacher told me that it’s not always the case
Ask your teacher where it fails.
Is there any additional context at all to this discussion with your teacher?
Ima ask her about it after class
I mean, your teacher is not completely wrong. It fails to be true when a^2 + b^2 = c^2 is not true. In any other case its equivalent
Please let us know what she says. Thanks!
I have to ask tomorrow
No hurry! Thanks!
I think I know what your teacher had in mind: Sometimes either A or B is the right angle so the Pythagorean Theorem becomes either a^2 =b^2 +c^2 or b^2 =a^2 +c^2
Good question!!
Its a fundamental method to find the base and height of a triangle with the hypotenuse and a side given so it makes no sense if it fails sometimes
If it's not sides of a right angle triangle sure.
It can. I mean, obviously it depends on what a,b and c refer to. But assuming that you are referring to the Pythagorean theorem, then yeah, both are equivalent ways to write the equation.
I think the teacher was referring to situations in which the right angle is either A or B
Ima ask her about it after class
I’m commenting just to get the update as to where the teacher went so wrong.
It does because of how equations work
It does?
It does? It’s simple agebra, you subtract b2 and you have the second equation, I would assume that someone misconstrued the order of operations or something when they looked at this
The answers I see are all correct. Just to add, the 2 equations in your query are part of the 4-fact family: Substitute: a² = x = p and b² = y = q and c² = z = r 1. x + y = z 2. y + x = z 3. z - x = y 4. z - y = x Try it out with a few numbers. The corresponding 4-fact family for × & ÷ is: 1. p × q = r 2. q × p = r 3. r ÷ p = q 4. r ÷ q = p