Art of Problem Solving: Classifying Quadrilaterals

Art of Problem Solving's Richard Rusczyk classifies some quadrilaterals.

[@JoesWife1000]

My 3 kids and I all enjoyed this. Thanks for making it fun!

[@kelyta3000]

Well done!! Interactive and fun.

[@kami69823]

Isn't the definition of trapezoid 1 pair of parallel sides, because parallelograms are 2 pair of parallel sides

[@understandingmaths1033]

Interesting, but not only controversial, also incomplete. Don't forget the kite! Kite should be same level as the trapezoid. Underneath the the kite is the rhombus. ie, rhombus is not only a special type of trapezium, it's also a kite. This means completely redrawing the relationships I'm afraid.

[@aw3156]

I skipped to the end and I was like this guy took it too far

[@luving4kitty]

Andy Wu LOL SAMEEEE

[@syamazaki6871]

Great explanation. I'm going to show my second grade class.

[@andrewbukowski5287]

he looks like the guy from blues clues

[@nikkigray4860]

yea

[@Bacon69363]

He does

[@211potomacct]

i like ur video, it really helps me understand it better!

[@blockytheblock1]

But at that point, it's parallel, so in your world, what defines a trapezoid? certainly not all parallel... right?

[@toebel]

Trapezoid = At least one pair of opposite sides parallel

[@angiedurand972]

what does 2 years of latin have to do with the word rhombus

[@jangwoo24]

That isn't a rectangle, the angle is slightly less and more than 90

[@Mr.Miles.]

Who’s here for school

[@missanadiaz]

Thank you! My students loved this video!

[@anilshiv45]

Brilliant !

[@mahashurbaji4724]

Please .. What is the name of this program? Thank you

[@veetoe4836]

Art of Problem Solving omfg read the title

[@isabelln804]

i love this!

[@anticorncob6]

Somewhere between you and khanacademy, would be the perfect teacher. Do you know the arguments as to why a parallelogram shouldn't be considered a trapezoid?

[@joharimalik1299]

The rationale for not considering a parallelogram a trapezoid is that the definition for a trapezoid is a quadrilateral with one pair of parallel sides. As in EXACTLY one pair, not AT LEAST one pair. Parallelograms have two pairs of parallel sides, and therefore don't meet those requirements. It's like when classifying triangles: an isosceles triangle has two congruent sides. According to the rationale in this video, an equilateral triangle would also have to be an isosceles triangle because it too has two congruent sides; the fact that the third side is also congruent doesn't mean that the first two sides stop being congruent. But the definition of an isosceles triangle isn't two OR MORE congruent sides, it's two congruent sides.Three is not two, so equilateral triangles are not a subset of isosceles triangles. Back to the quadrilaterals: trapezoids have one pair of parallel sides, not one OR MORE pairs of parallel sides. One and only one. So parallelograms, which have two pairs of parallel sides are not actually a subset of trapezoids. Hope that explanation of the logic behind the great trapezoid-parallelogram schism helps :)

[@anticorncob6]

Johari Malik So why does the definition state that a trapezoid can only have one pair of opposite sides? Almost every theorem about trapezoids also applies to parallelograms. And I don't think the definition of a trapezoid is universally agreed upon, just like how there is no universal agreement on what a natural number or whole number is.

[@joharimalik1299]

***** I was explaining this particular line of logic, whereby one pair means exactly one pair, not endorsing one view over the other. I understand that this isn't a universally agreed upon thing, especially when it comes to quadrilaterals.

[@joharimalik1299]

+anticorncob6 Right, it's not universally agreed upon. But your question that I responded to asked for the arguments for why a parallelogram wouldn't be considered a trapezoid. That's what I addressed.

[@gmhiede1468]

Thank you!this help me for my math problem💗💗

[@toddlisella988]

Love it, great job! The quad in the top left could almost be a kite

[@jimmygeis8951]

I thought today we had to watch the cursed “math antics” thankfully we got to watch this instead

[@mariagracia8133]

FineBrother Cringe you need to do E learning? XD

[@jimmygeis8951]

Isabella Sofia sadly

[@mariagracia8133]

FineBrother Cringe me too :(

[@SSJ28K]

we had to do both

[@ryuryu8280]

My math teacher put this on his blog

[@temiade1]

Dumachew Anime good. job

[@paper6005]

same

[@naomibrannan8382]

same

[@kboardist]

AWSOME

[@jacobbastian7714]

I agree with you

[@temiade1]

Jacob and Abbie good

[@divinepeace007]

ur very kid and gentleman and good teacher

[@kourtnussy9707]

yes he is very kid

[@bandsweretaken2705]

what are u using

[@xplicit6106]

ikr i never thought that there was that technology in 2012

[@socksnotemo7980]

Shout out to Mrs. Zarns class!

[@andrewpeterson4471]

+Izi Smith YASSS!!!!

[@alexwang982]

I’m in that class

[@yashin2068]

tnx man, great explanation ;)

[@yashin2068]

@Isabella Warner yes my teacher asked us to watch it :)

[@adebayotaiwo3072]

Interactive fun😮😃

[@donovanwyatt4730]

#TrapezoidsArePeopleTo

[@ryuryu8280]

lel

[@alexwang982]

*too

[@M_Chen333]

#TrapezoidsAreParallelogramsToo

[@mintyt1942]

Watching this for me

[@kboardist]

OOOH! smart

[@laurarivas4385]

I love math

[@janaegreen2746]

Nice

[@slongz2750]

Im confused

[@kboardist]

NICE

[@soarstudios7325]

yes

[@andrewwwrightt151]

hi

[@kboardist]

COOL

[@tscottj23]

i like it it cool

[@elijahestes1083]

106 plus 74 is not 108

[@43Cubes]

he said 180 not 108

[@kboardist]

WOW

[@the1andonlyLeta00]

I would have loved to show this video to my deaf and hard of hearing students but unfortunately there were no captions... what a shame :(

[@averyinterestingpineapple6038]

L

[@GSHAPIROY]

What about triangles? Isosceles triangle means two sides are equal. Equilateral triangle means all three sides are equal. All equilateral triangles are isosceles. Scalene triangle means no sides are equal. We could use your logic with the trapezoids and parallelograms to say that all triangles are scalene.

[@dav87x]

You could actually. You don't ever use scalene triangles outside of classification if you think about it, you use a "general triangle".

[@maangelessebial2423]

180

[@kboardist]

OOOOOOOOOOOOOOOOOOOHHHHHH

[@kboardist]

!

[@sanghoonjung921]

Then I guess that his world is quite small

[@ryuryu8280]

yep

[@peter_castle]

indeed, the earth is small in the universe

[@kboardist]

MMMMMMMMM

[@benjamingillin5328]

kidz show maan. thiz iz four for year olds.

[@abhirupan7630]

You should get your spellings right first.

[@slongz2750]

Your spellin doe

[@kboardist]

@@slongz2750 .

[@kboardist]

NA NA NA NA NA NA NA what you get for making fun

[@gnomey5421]

2 years of latin wasted

[@nickgill6639]

Wait a minute rhombus have equal sides but it doesn't have equal angles and square have equal sides and equal angles than how could they be same in your world 🙄

[@kboardist]

!