/sci/ - Science & Math » Thread #13979391

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proof of perpendicularity

Anonymous Sat 18 Dec 21:34:04 2021 No.13979391 View Reply Original Report

Quoted By: >>13979416 >>13979426 >>13979461 >>13979592 >>13979801 >>13979869 >>13984104 >>13984169 >>13984642 >>13984655 >>13985471 >>13985541 >>13986740

How do you prove that two lines are perpendicular without measuring their angle?

Anonymous

Anonymous Sat 18 Dec 2021 21:39:22 No.13979416 Report

Quoted By:

>>13979391
Eyeball it. If it were good enough for yer ancestors it ought to be good enough for you.

Anonymous

Anonymous Sat 18 Dec 2021 21:41:48 No.13979426 Report

Quoted By: >>13979456

>>13979391
Draw a vector on each line and take the dot product. Or if you know the slopes, check that if one line has slope m the other has slope -1/m.

Anonymous

Anonymous Sat 18 Dec 2021 21:47:56 No.13979456 Report

Quoted By:

>>13979426
the dot product only works if there is a system of rectangular coordinates.

Anonymous

Anonymous Sat 18 Dec 2021 21:49:34 No.13979461 Report

Quoted By: >>13979540

>>13979391
Construct a perpendicular bisector to line AB through C and see if it agrees with the other line

Anonymous

Anonymous Sat 18 Dec 2021 22:05:35 No.13979540 Report

Quoted By: >>13979566

>>13979461
but how do you know if the bisector is perpendicular?

Anonymous

Anonymous Sat 18 Dec 2021 22:12:25 No.13979566 Report

Quoted By: >>13979596

>>13979540
ruler and compass i.e. using the other line as reference for the construction for the new line

Anonymous

Anonymous Sat 18 Dec 2021 22:18:40 No.13979592 Report

Quoted By:

>>13979391
draw a square on it.

Anonymous

Anonymous Sat 18 Dec 2021 22:19:08 No.13979596 Report

Quoted By: >>13979649 >>13981926 >>13984642 >>13984888

>>13979566
the post says without taking angle measurements, I want a logical and rational proof without having to measure it

Anonymous

Anonymous Sat 18 Dec 2021 22:25:47 No.13979625 Report

Quoted By:

Pythagorus.

Anonymous

Anonymous Sat 18 Dec 2021 22:30:23 No.13979649 Report

Quoted By:

>>13979596
so evalute an inner product
by virtue of the lines existing, there must be a vector space they span. so you can lay two vectors on the lines and evaluate to 0 showing they are perfendiicular.

Anonymous

Anonymous Sat 18 Dec 2021 23:00:32 No.13979801 Report

Quoted By:

>>13979391
dot product

Anonymous

Anonymous Sat 18 Dec 2021 23:04:34 No.13979817 Report

Quoted By:

You use point-slope equation

Anonymous

Anonymous Sat 18 Dec 2021 23:07:04 No.13979824 Report

Quoted By:

https://www.youtube.com/watch?v=CXcFN9KhIsA&ab_channel=ProfessorLeonard

Anonymous

Anonymous Sat 18 Dec 2021 23:08:19 No.13979828 Report

Quoted By:

What information do you have about the lines beyond the drawing?

Anonymous

Anonymous Sat 18 Dec 2021 23:17:53 No.13979869 Report

Quoted By:

>>13979391
Given lines A, B.
Use a compass and straightedge to construct a perpendicular line (C) and a parallel line (D) with respect to line A. If the line segments of lines D and A between lines B and C are equal, then lines A and B are perpendicular.

Anonymous

Anonymous Sun 19 Dec 2021 11:23:13 No.13981926 Report

Quoted By:

>>13979596
ruler and compass has no angle measurements. your are just using properties of circles to create a perpendicular line or a normal line. if the two lines aren't a function and have no angles there is just no other way to tell.
the reason it works is because of euclids axioms

Anonymous

Anonymous Sun 19 Dec 2021 21:25:44 No.13984104 Report

Quoted By:

>>13979391
>without measuring their angle?
Start on a line,
travel to the intersection and make a 90deg left turn,
traveling same distance and stop and make another left turn
traveling same distance and stop and make another left turn
traveling same distance and stop
If you end up in the same place you started and you traveled equal distances on both lines it means the lines are perpendicular.

Anonymous

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Anonymous Sun 19 Dec 2021 21:37:23 No.13984169 Report

Quoted By: >>13984902

>>13979391
Make 4 points on each ray equidistance to the center of the point.

Make a shape connecting the 4 points.

If the shape is a square (all 4 sides equal length), the lines are perpendicular.

I came up with that one on the toilet and I feel like it would work.

Anonymous

Anonymous Sun 19 Dec 2021 23:13:02 No.13984642 Report

Quoted By:

>>13979391
>>13979596
It all depends on how you *describe* them.
In math, you never work with objects themselves; you work with their descriptions.
If you describe these two lines as equations like y = ax+b and y = cx+d, then the way to prove it is by multiplying ac and seeing if it equals -1.

What are these two lines in the picture? Describe them for me in such a way that I myself can reproduce them.

Anonymous

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Anonymous Sun 19 Dec 2021 23:17:17 No.13984655 Report

Quoted By: >>13984665 >>13984897

>>13979391
With a compass draw a circle centered at O with an arbitrary radius, the circle will intersect the line r at the points A and B; now draw two more circles centered at A and B with radii equal to each other but greater than the segment OA, they will intersect each other at the points C and D. If C and D lie on the line s then r and s are orthogonal to each other

Anonymous

Anonymous Sun 19 Dec 2021 23:20:12 No.13984665 Report

Quoted By:

>>13984655
Forgot to mention that O is the point of intersection between r and s

Anonymous

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Anonymous Mon 20 Dec 2021 00:04:36 No.13984888 Report

Quoted By: >>13984902

>>13979596
>the post says without taking angle measurements, I want a logical and rational proof without having to measure it
Pic related doesn't require measuring angles. It's also a carpentry trick to make sure something is square.

Anonymous

Anonymous Mon 20 Dec 2021 00:05:28 No.13984897 Report

Quoted By:

>>13984655
This is the way.

Anonymous

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Anonymous Mon 20 Dec 2021 00:06:43 No.13984902 Report

Quoted By:

>>13984888
wtf carpenters stole my proof >>13984169

Anonymous

Anonymous Mon 20 Dec 2021 00:14:11 No.13984944 Report

Quoted By: >>13985617

Measure slopes of both lines.

If line A is the opposite reciprocal of B line, they are perpendicular.

Anonymous

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Anonymous Mon 20 Dec 2021 02:34:29 No.13985471 Report

Quoted By:

>>13979391
Sqrt(172^2+280^2) = 328.6

pythagorean theorem is the most fundamental theorem in geometry

Anonymous

Anonymous Mon 20 Dec 2021 03:02:54 No.13985541 Report

Quoted By:

>>13979391
Suppose a line B is to be checked for perpendicularity to a line A. Draw a line parallel to A. If B is the shortest line between the parallel lines then it is perpendicular to A.
Another way to test this is to fold Line B where the crease is line A. If B is perpendicular line, then B will lay on itself.

Anonymous

Anonymous Mon 20 Dec 2021 03:33:29 No.13985617 Report

Quoted By: >>13986672

>>13984944
Measuring the slope is cheating, as it is correlated with an angle

Anonymous

Anonymous Mon 20 Dec 2021 09:58:10 No.13986672 Report

Quoted By:

>>13985617
You can easily measure the slope without an angle if you have two points

El Arcón

El Arcón Mon 20 Dec 2021 10:34:58 No.13986740 Report

Quoted By:

>>13979391
the dot product of the tangent vectors is zero if they are perpendicular

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