Proof: perpendicular lines have negative reciprocal slope | High School Math | Khan Academy
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- เผยแพร่เมื่อ 20 ส.ค. 2024
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Sal proves that perpendicular lines have negative reciprocal slope using triangle similarity.
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That's amazing Sal :) thank you . Everyone needs a math teacher in order to love the math . 👍
Nice proof. You can prove this result with Pythagorean Theorem as well.
Thank you so much! When I asked my teacher, she just replied with “it’s a rule. If you’re not satisfied just look it up yourself”
Woah that's such a wrong thing to say😢
The arrow written at 7:12 looks like a smile face :D
Blew. My. Mind. I never thought about it that way.
Kinda confused on why CB is positive but DE is negative. I understood everything else but not that. Thx for the videos guys, I love your work.
CB isn't positive, but CB and AB are both negative, since AB is to the left of the horizontal line. So when he takes the ratio, he divides the two numbers and then the negative signs cancel.
+Reeta Singh Oh that makes a lot of sense, now I completely get it. Thx a lot for the quick and clear response :)
Gonzalo Kuwae None of these lengths are negative. Negative length means nothing in this context. What Sal is talking about is change.
The whole number 6 is neither positive or negative. It's just six of something.
The integer +6 means change in a forward / positive direction, what have you. Depends on your frame of reference. The integer -6 means change in a backward, negative direction.
If I have a flag pole, and the height of the flag is 10 ft, but then I raise it to 16 ft, by how much has the height of the flag changed? It has changed by +6 feet. Change is defined by convention as final minus initial. So the final height is 16. The initial height is 10 ft. So final minus initial = 16 - 10 = 6.
Similarly, if the flag pole starts at 13 ft and I raise it to 9 ft... Notice here I can still say raise. It's just raise in the other direction. You can also say negative growth. Anyway, final minus initial = 9 - 13 = -4. The height of the flag has changed by negative 4 ft.
So re watch the video. And track which points we're moving between track the change. :)
Line cl is moving upwards to the right which will give out positive change in x and y but line ME is moving downwards to the right will will give positive x but negative y because y is being decreased while the line move downwards....
Great video, perhaps this suggestion is useful to someone :
I find that it makes the relationship between the similar triangles and the lines more obvious if you start with one right angle triangle, laid down with the x and y axes aligned with the short sides, then take an identical triangle and rotate it by 90*. The two lines are the hypotenuse of these two triangles and are at right angles to each other by construction. Not only are the triangles simular but they have equal sides. If my description isn't great, I apologise, it's super intuitive when you do it, especially if you have some physical triangles (eg bits of paper) that you can rotate. Also good for proving pythagoras.
When sal takes --slope of m-- he takes DE as negative (i.e -DE/AD) , but when by AS A criterion he proves EDA~ABC he then writes DE negative (i.e CB/BA=AD/DE
Why ??
Because it the slope case he’s taking about change of y but in the other case he’s talking about lengths
A much easier proof is to realise that the slope of l is tan a where a is the clockwise angle between l and AD and the slope for m is tan(-b) where a+b=90 so tan(-b)=tan(a-90)=sin(a-90)/cos(a-90)=-cos(a)/sin(a)=-1/tan(a).
I'm absolutely lovin' it.
Interesting 😮
Great video
incredible
Very clear and nice proof
Loved this
Great proof, thank you!
Thank you very much!
I love this proof
this is beautiful
Wow it's really awesome
Great sal sir
"Cb"and "de"both are decreasing....., gotchhaa x is alo in -ve and y in -ve so cancel out
great.
thanks for uploading 😊❤
Thanks sal😊😊
Yeah, good! Just use the transformation theory - > rotation 90 degrees
wow
how do you do that
90°
😮
your x sometimes looks like a z :)
Just for kicks, lol