I’ve always heard the shortest distance between 2 points is a straight line. But if thats true then how does the A^2 and B^2 parts of a triangle factor into that? Wouldn’t they also be the shortest distance between 2 points?
Edit: I’m trying to put this into walking perspective, actually hay stacking. Say I have a bale of hay in the very center of the field. I need to take it to the very southwest corner of the field. You’d think just taking the hay in a straight line (directly southwest from the center) would be faster than going to the very south of the field, and then the very west of the field until you reach the stack. Wouldn’t both ways you go be the same distance? So therefore the shortest distance to between 2 points isn’t JUST a straight line, it’s also a right angle?
In: Mathematics
So, yes, A and B are the distance between 2 points each. But, A and B represent 2 separate lines. A is between point A1 and A2. B is between A2 and B1. Pythagorean theorem is trying to find the line that exists between A1 and B1, a previously unmeasured segment.
Edit: Daw two lines that form a right angle, label the points A1, A2, B1. Then draw the third line between A1 and B1 — this is the line you’re trying to find the length of.
Hope this makes sense. Basically your question is asking about something the theorem isn’t about.
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