Vector Geometry Proofs (1 of 3: An unexpected quadrilateral property)

[layer]

Thank you for all your help. Really helped through my A level maths and further maths but I wanted to ask if there were gonna be more videos on 1st and 2nd order DE's later on? Once again thank you ❤❤

[PhilipMurphyExtra]

Saw a link to this somewhere so decided to check this out.

[jhouck]

The geometric proof needn't be that complicated - if you join O to P it's trivial to show the smaller triangles at the top and bottom are similar to the two larger triangles created by OP, and because those smaller triangles are formed by joining the midpoints, the sides similar to OP must each be half the length of OP and parallel to OP (and therefore each other).

But yes, using vectors gets you there faster since vectors incorporate both direction and magnitude.

[vmrxsoi]

was this an online class or something which he recorded???cause i realy like the old ones which he recorded in the classrooms...not that i dont like these'

[LamontJackieMontgomeryMelvinHo]

That looks like a irregular quadrilateral(a trapezium).

[anjaligupta]

Sir please show the proof of how AC and BD are equal and parallel

[ojorimw]

what grade do u learn this types geometry math?

[BlueGiant]

2:09 How is it that in the 21st century a mathematics teacher with an iPad does not have a software tool for measuring and/or marking the midpoint of a line segment?
Using tilde to denote a vector is new to me but it seems to be becoming common since it's listed as a use for tilde and examiners are deducting points for not using it.
I'm wondering if the proof would be any shorter using Geometric Algebra notation.

[scipie]

Can't I just split the quadrilateral horizontally and vertically and show that I have two pairs of parallel mid segment which is the definition of a parallelogram!

[goreacraft]

He cut the video at the end when the student answers with "No!" 13:51