4, 6, 11 triangle, MOST don’t know the reason why this is NOT a REAL triangle

[@walterbrown8694]

For a 3 sided polygon to be a triangle, the sum of the lengths of the 2 shortest sides must exceed the length of the longest side. The example shown in the illustration, sides, 11, 6, 4, does not meet that requirement, hence the figure is not a triangle.

[@richardrigling4906]

What if you're plotting on a non Planar surface? The basic assumption is plane geometry. This shape is possible on a sphere.

[@walterbrown8694]

Yeah - I could be wrong , but I have a sneaking suspicion why the high school math course I took over 70 years ago was called "Plane Geometry"@@richardrigling4906

[@richardmelville5973]

@@richardrigling4906 If it isn't on a plane, it isn't a triangle.

[@toughenupfluffy7294]

Stereographic projection.@@richardmelville5973

[@toughenupfluffy7294]

The figure is a triangle; the measurements are incorrect.

[@danieldennis9831]

It can't be real because a+b cannot be < c (where c is the longest side and a and b are the other sides).

[@DdDd-ss3ms]

The reason is not because these rules... these rules are a result of the reason ! The reason is way more simple. If you imagine you 'flatten the corner between the 4 and 6 leg to (almost) 180 degrees, the 4 and 6 legs would be (almost) a straight line and parallel with the 11 leg but will only have a length of 10 . from this we can make the rule the sum a + b must be greater than c . Some talked here its possible for curved lines. Imagine this triangle is on the surface of a sphere with radius R What would R be to make this triangle possible?🤔

[@cheriem432]

As an engineer I really like your channel, but in trying to make your videos interesting, you take too long to get to the point. All the additional talk doesn't help people who need to understand this. Perhaps explain how to solve the problem and then add the rest of the monologue for those who are interested?

[@stephenbryant7189]

As someone with a poor memory, who couldn't be an engineer even if he could live his 69 years over from birth, I really love the built-in "redundancy". I even wish the video background were a unit circle template with trig functions.

[@litasanford7595]

I disagree. As a teacher, I can tell you w/o hesitation that showing every step at a speed that everyone can follow, allows you to reach every student. When students understand each step, they can work through even complicated problems with confidence, gaining in self-esteem. Math * thorough instruction = more mathematicians, happier kids & more competent citizens

[@robertsullivan9833]

you can always fast forward as needed

[@poetjenoetje]

​@@robertsullivan9833that's what I do bc it's wayyyy too slow for me too

[@MsChemicalEngineer]

I hear you, I just want him to get to the point!!! Engineers use math every day, it's our tool kit!!

[@Kamabushi999]

A bit winded and if you watch one video is ok but after so many videos it creates anxiety but actually I still enjoy the videos You are a treasure I wish I had you as my teacher in 9th grade I had a lady back in 1974 that confused the crap out of me but I don’t blame her 100% More like 50-50 I needed a tender touch back then. You are a great teacher.

[@disraelidemon]

You can also disprove the triangle by construction. Draw an 11cm line and then a 4cm radius circle from one end and a 6cm radius circle from the other. Where the two circles intersect would be the third vertex of the triangle, except the circles don't intersect.

[@mikekelly5869]

Simplest way to teach this is to rotate the two short sides around the intersecting angle using a series of sketches, illustrating that the triangle becomes a straight line when the length of the long side equals the sum of the lengths of short s1des

[@melissalevine2373]

Many students need the explanation. It may be long to some, but totally necessary for certain learners.

[@louisepeterson6626]

6+4 = 10 and 10

[@Scott-i9v2s]

... must be =< sum of other sides

[@nicetasgrass1813]

I’m thankful that I’ve found your channel ,it’s really a big help to me!❤

[@jonathancapps1103]

I didn't know the term "triangle inequality," but I recognized that with two legs of lengths 6 and 4, that the 3rd leg must be smaller than 10.

[@N269]

Simples, 6(adj)+4(opp) == 10, take the hypot,11, and rotate, still 11.... absolutely absurd measurements.... 10

[@johnhewett9483]

sir you have the unusual ability to make a long complicated video out of something so simple and common sense

[@barbarasnetiker3452]

No, he's actually explaining it in simpler terms to those who are somewhat mathematically inept! If I had had math teachers like him when I was in 7th or 8th grades, I would have gotten better grades in Math! Unfortunately, I didn't have great Math teachers until I got to high school, because they took the time to explain things!

[@MrMousley]

Normally his long explanations help people understand, but in this case I have to agree. It took over 8 minutes to say .. ''With a triangle the 2 shorter sides added together have to be longer that the longest side or they won't form a triangle''

[@DdDd-ss3ms]

@@barbarasnetiker3452 he makes math why lot of children are afraid for math because they do not 'see it' and are confronted with 'rules' . Better to make it visual , make the triangle flatter till the short legs almost reach the long leg. then you see the long leg must be shorter then the two short legs together. (explain it with some sketches like some one else here sugested) . AFTER this give the legs names like a , b and c and write what the visualisation showed us in a rule form "the long leg must be shorter then the two short legs together." c < a + b or a + b > c

[@jayrussell3796]

​@@DdDd-ss3msHe explains things perfectly. You just don't have patience. Trying to explain and teach math quickly is like trying to explain and teach how to tie your shoes. There are steps involved that can't be left out.

[@DdDd-ss3ms]

@@jayrussell3796 is not about quick or fast explaining. Its about presenting thing in a complicated way or being able to present complicated things in a simple way. To let your students gain insight you must be able to peel like an onion the problem to simple sub problems. . What happens in this video is not peeling the onion but putting morelayers on it

[@aaronbredon2948]

In any polygon, the lengths of all the other sides must be greater than the length of the longest side. When this is not true, you cannot complete the polygon. If they are exactly equal, you have a line.

[@glenwardgross366]

I leaned the Pythagorean Theorem at about the age of 9 because on Saturdays I worked with my family whom were in the trades.

[@simonallanby5945]

It’s not a right angle triangle.

[@johnhewett9483]

the sortest distance between two points is a straight line 11 is greater than 6 plus 4 problem solved

[@ingsve]

One easy way to think of it is that one side of a triangle always equals the shortest distance between two points and following the other two sides must then be a longer path between those two points. So if you have one side that is 11 that is the shortest path then going the two other paths must be longer than the shortest path but since 6 and 4 is not longer it is not a triangle.

[@ed_ward_1430]

The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two adjacent sides. (3-4-5 rule) - Pythagorean Theorem.

[@toughenupfluffy7294]

As he pointed out, this is not a right-angled triangle.

[@johng.1703]

the combined length of A & B is shorter than H so there is no possible angle of A & B that these 3 lines can connect to form a triangle, if they were equal they would just make a straight line.

[@Scott-i9v2s]

It would LOOK like a straight line. But that does NOT mean that it IS a line instead!

[@davidhitchen5369]

In general, the longer side must be smaller than the sum of the other two. If the smaller sides are 4 and 6, the longer side must be less than 6+4 = 10

[@glenwardgross366]

Great John. BTW 6-8-10 will work just like your 3-4-5. How interesting is it that our 1-10 number system has 6 number that makes the Pythagorean Theorem. Also if you add zeros to infinite to the 3,4,5 or 6,8,10 it will always equal a right triangle. My livelihood depended on me knowing the Pythagorean Theorem.

[@jeanettes427]

Hi Mr. KZbin Math Man, I am also thankful that I’ve found your channel. They are so helpful! Could you do a video explaining scale factors?

[@themister3865]

Before reading the answer, I think the length of the longest side must be shorter than the sum of the lengths of the two shorter sides in order to construct a triangle. Because 6 + 4 =10 is less than 11, you cannot construct a triangle with these three leg lengths.

[@themister3865]

Opps. I was incorrect. After watching the video, I now understand that the sum of the lengths of any two sides must be greater that the length of the remaining side. I get it now. I was on the right track but neglected to apply the same rule that I applied above in my initial answer two more times. hahaah You got me! I did however discover the calculation of why this failed to be a triangle. Do I get partial credit? Maybe a B+ but no certificate of excellence for the correct answer.

[@harrymatabal8448]

In simple language, two sides of a triangle are together greater than the third.

[@almoemason]

Thanks a lot guys. My son was trying to figure this one out. His head exploded. You should put a WARNING on your site.

[@RichardFay]

The shortest distance between any two points is a straight line. Therefore the longest side (a straight line) must be shorter than the other two sides combined. 11 is NOT shorter than 4 + 6.

[@russelllomando8460]

2 sides must add to be greater than the other.

[@ahab8997]

That explained it in less than 3 seconds 😊

[@claytonbenignus4688]

Not possible in Euclidean Geometry. Maybe possible in Spherical Geometry.

[@chrisreed208]

Why can't I find the length of the hypotenuse. 1/2 the base X the height.

[@stephenmcleod3348]

I'm a history major, but want to amen the engineer's comment on verbosity. I've learned a lot of math OJT as a self taught computer systems engineer.

[@thenetsurferboy]

Do not call yourself an engineer if you are self taught I am a doctor self taught

[@alittax]

​@@thenetsurferboy I don't think they're the same. You can only be a professional in both if you've had practice. You can practice engineering questions, as they do at university. But you can't practice on live patients.

[@thenetsurferboy]

@@alittax I do I do not know what you are referring to.

[@alittax]

@@thenetsurferboy Your comparison between being a self-taught doctor and engineer. Or wasn't that what you originally meant?

[@thenetsurferboy]

@@alittax You are totally confused

[@sudhawahal1612]

Sum of shorter sides is always greater than d third

[@TheSimCaptain]

Shortest distance between two points is 11. 6 + 4 add up to 10.

[@jgar611]

What measuring system are you using? You can complicate mathematics to the point where people give up. When this is done its little more than an exercise of a narcisstic mathematician.

[@charlottehayward5943]

I was never good at math but I'm enjoying brushing up.

[@veebee9785]

Love the channel....not bothered by the extra talking. I just fast forward and so can you!!!!😊

[@teenasmith8936]

I'm just starting to review you explain things well thank you

[@royschering1140]

Sum of the two shorter legs must be greater than the long leg. If the sum equals the long leg, then the triangle becomes a line.

[@devonwilson5776]

Greetings. The value given by the hypotenuse does not conform with the Pythagoras theorem.

[@jgar611]

Precisely!

[@StormyMonday0896]

A squared + B squared = hypotenuse squared

[@andrewbarnett84]

It is possible if the "11" side is a curve. There was no reason it has to be a triangle, however it could be a slice of a pie.

[@sdragut]

the square root of the hypotenuse must be equal to the total square root of the adjacent sides. 36+14= 50. square root of 50 is 7.07 not 11

[@SylviusTheMad]

It is possible, as long as it's non-Euclidean.

[@vee8217]

The 2 shorter sides when you add them up together it should be more than longest side 4+6

[@homeauburnRaja-hm3gq]

Basically it is for teaching the ways to solve problems

[@seesafar9912]

The hypotenuse does not equal the square of the other angles.

[@-theflea-4561]

It can be a real triangle, but you need curved space to make it work

[@jgar611]

Any polygon with only 3 sides is a triangle with all internal angles having a total of 180 degrees when added together.

[@jgar611]

Want to try some trigonometry?

[@jgar611]

Sorry about spelling😂

[@TorchwoodPandP]

A triangle has three ‘angles’, as long as you don’t expect one angle to be 90°, it can exist! The sides don’t even have to be straight lines.

[@KNKLHEAD]

My first thought was increase the angle so that the 11 fits in there ... then realized if you increased the angle the two side only add up to 10.

[@cheriem432]

. . . and I don't understand why you say that the first is not an "*actual real triangle*". A triangle is defined as 'a closed plane figure having three sides and three angles'. This figure qualifies with this definition.

[@barbarasnetiker3452]

Just because he drew it to look like all 3 sides closed, the actual length of each side have to be able to physically close.

[@marthakratz7877]

​@@barbarasnetiker3452 If he gave us incorrect lengths for any of the sides that does not stop it from being a triangle.

[@q.e.d.9112]

It’s pretty damn simple. If the combined length of the two shorter sides is less than or equal to the length of the longer one they cannot make a triangle. If it’s greater, they can.

[@Scott-i9v2s]

Your "less than or equal" is NOT correct. Just "less than" would have been correct. Ditto your "greater" should be "greater than or equal to". Your teacher was forced to adhere to an incorrect curriculum.

[@Geoff_G]

11 > (6+4)

[@peteranserin3708]

All triangles interior angles equal 180 degs.

[@mikespencer4922]

Pythagoras.... the sum of the squares of the opposite sides equals the square of the hypotoneuse..... not so here.

[@berndhutschenreuther8342]

It is not possible in Euclidean geometry, that is trivial. But is it possible in other geometries? As far as I see, the sides are warped in your screen. We can see this because 4+6=10 < 11. In your painting it is a triangle, so it must be warped.

[@malcolmbrewis5582]

Are you referring to spherical geometry.? 🤔

[@berndhutschenreuther8342]

For example, yes. There additionally exist very other forms like TaxiCap or Manhattan geometries.@@malcolmbrewis5582

[@Scott-i9v2s]

@tabletclass You have 3 errors at 3:57. None of the 3 ">" symbols is correct. All 3 must be "equal or greater" (or "not less than") symbols. If the sum of 2 sides is equal to the 3rd side, then it is *still* a triangle. Just because it *looks* like a line is *not* sufficient to exclude it from the class of triangles. Or from the class of Klein bottles, for that matter. This also means that such a triangle will *not* automagically *become* a line *instead* (ie lose the capability of being called a triangle). (See there the cause of the myth that a 3-sided shape must have a not-zero area to be called a triangle.) Actually, even a single point can be a perfectly valid triangle (or quadrangle, toroid, &c). Just because a side of a shape has a length of 0 is not a valid reason to *not* call it by the name of said shape. *Starting* the teaching by *including* zero-length sides makes later-on learning about limits much more intuitive, with *no* need to break pounded-in habits. Methinks that subconsciously teaching that to call a shape by a certain name it must be *visible* as such is a disservice to the students. This method of teaching perpetuates the concept of "degenerate" shapes, a concept that is not necessary for correct understanding. One starts *past* the subject's true starting-point when teaching via this method. And then later-on must break learned habits when introducing more-basic stuff. Example: The "You cannot add 3 apples and 5 oranges" thingie will *not* come up when teaching sets *before* (for instance) addition. All-in-all, my opinion is that in at least the USA the whole educational system is based on not-valid curricula. Curricula designed by people who are not-sufficiently trained in the field. No wonder that so many teachers in the USA teach incorrectly, since they must heed the curriculum. Also no wonder that so many teachers in the USA are *not even aware* that they lack the necessary knowledge...

[@tunneloflight]

actually it is. But only in certain non-euclidian spaces.

[@SherriRounds]

A2+B2=C2

[@panlomito]

If the 4 side is turned almost flat (in line with the 6 side) the length of C < 10 so C=11 is not possible.

[@timothyroarke6072]

Yes, you take waaaaay to long to get to the lesson.

[@robertgross578]

In any triangle, the sum of any two sides must be greater than the third side.

[@timper4326]

4 and 6 is not a right angle, is it obtuse?

[@Danielle-nz9tn]

The shortest route between two points is a straight line; however, in this triangle the distance of the straight line (11) is longer than if one took the “scenic route” down the side labeled 4, then turned the corner and went down the side labeled 6. Does not make any logical sense.

[@wes9627]

This is like I can't get both ends of my belt to meet up anymore. My wife says it's because the sum of the two sides don't add up to my girth.

[@brendapatterson682]

Sides not equal?

[@theeardrafter]

I stand corrected

[@rodneytopor1846]

Because the shortest path between two points is a straight line.

[@Davidbmr1970]

a+b cannot be shorter than c.

[@RichZFishes]

Because the longest side must be greater than the length of the other two sides combined. I would think anyone who made it through grammar school would know that.

[@margritkaminsky1470]

Wow, thank you.

[@bosoerjadi2838]

The thing is, that, when you'd ask someone to actually draw such a triangle, he'd immediately recognise the impossibility and, soon after, he'd have discovered the rule entirely on his own.

[@zadockreid3527]

The sum of the 2 smaller sides not equal to the length of the longest side.

[@argonwheatbelly637]

The sum of the length of the sides can't be less than the length of the hypotenuse. Took slightly more than two seconds to see that.

[@Ivanxxyyzz]

I learned this in a course called “Plane Geometry” in 1958. I don’t think it’s being taught anymore. It was great for learning about how to think. Not really math in my opinion. Such a pity!

[@stevedietrich8936]

Simple. The sum of the two shortest sides are not equal to, or greater than, the length of the longest side.

[@Scott-i9v2s]

Yours is the 1st comment that I see that is COMPLETELY correct. The video is only partially correct.

[@jayrussell3796]

For those with no patience, imagine trying to teach how to tie shoelaces. Steps are involved and a thought process. You can't just skip to the end.

[@mvssarma3387]

Not possible. Sum of 2 sides is to be greater than 3rd

[@paulhaye]

A + B = C. I didn’t cheat. Am I wrong? Now I’m going to see what teacher said. Right angle triangle, right? I gotta touch up so I can teach my daughter.

[@Twilightzoneisreal]

Because b²+c² doesn't = ✓a 7.21 does.

[@raynewport9395]

It is a real triangle. You can see it. Therefore your numbers are wrong or misinterpreted.

[@melissalevine2373]

A+b is less than c

[@KarenStrube]

A=1/2 bxh

[@rebirth_mishap]

scalene triangle

[@cyruschang1904]

The sum of two sides of a triangle cannot be smaller than the remaining side Since 4 + 6 < 11, this cannot be a triangle

[@danmalim6919]

Right Angled Triangle more so.

[@siaripop7]

Square root of 16 + 36 = 7.211 After figuring it out he says it's not a right angle. Trickery at its best!

[@DeereX748]

The triangle shown could not possibly have the lengths listed and therefore is extremely misleading. Certainly, the lengths given cannot form a triangle, as the two short sides have a combined length shorter than the long side.

[@anthonydenning5988]

All add up to 180 degrees

[@Scott-i9v2s]

Indeed. But remember that "0 + 0 + 180 = 180"... AND that the "sum = 180-degrees" is ONLY relevant in a plane with zero curvature.

[@Joe-qn3ou]

the inside angles need to equal 360 degrees

[@RobinLoxley-fn8ex]

Er.

[@elliotlambert3817]

Why not draw it to scale and not create a problem out of a trick.

[@harper626]

if the two shorter sides when added together are not longer that the longest side, it can't be a triangle

[@jimmyatnip2510]

You failed to indicate that the angle is 90 degrees, SO THIS IS POSSIBLE..... but the angle would be more than 90 degrees. I learned this when I was about 12 y.o. and learning carpentry. I was taught that 6, 8 & 10 would give me a 90 degree angle.... square walls when laying out the walls in a house. Later, in math class I learned the reason why.

[@thomasharding1838]

If you straighten out the two shorter sides, they would be 10 units long. The third side can't be 11 unless of course, it's curved. But then it wouldn't be a triangle. Enough said.

[@joanstehlik235]

I don't understand why you would multiply 7 by the contents of the parentheses???

[@rafyvele]

On a triangle any side must be smaller than the sum of the other two

[@NickWebber-vp4pd]

Because A+B≠C😮

[@jeffreyfoster8413]

Why did you not just explain that the shortest distance between two points is a straight line, and since if you let the 4 start at one end of the 11 and the 6 start at the other end they won’t touch and can not make a triangle.

[@canman5060]

Heron's Formula.

[@klangdownab910]

Clearly it is a triangle .what is wrong is the length of sides..it looks as though the 6 should more like 8 or 9

[@Ciarananthonymitchell844]

Triangles Create the Universe!

[@MladenČolić-u5t]

... and you need only 8:25 to explain why? Miraculously :P

[@rdspam]

Hmmm. Triangle Inequality is a pretty fundamental theorem.