@1:53 - you said: "And through angle chasing, we can see that this is a parallelogram." - THAT is the proof. It would have been nice to show an animation of that angle chasing.
@SuperYoonHo2 жыл бұрын
subbed!
@dnickaroo35743 жыл бұрын
Nice proofs.
@kanki_35203 жыл бұрын
Thanks man
@orion_2223 жыл бұрын
thank you.
@indian58774 жыл бұрын
♥️♥️♥️♥️♥️♥️♥️♥️
@Achill1013 жыл бұрын
@9:32 - "because angles CAD = DAB, the two arcs that they intercept are equal." - That is true but doesn't seem trivial to me. Is it? I saw that it's true by considering the angles at the center of the circle, R. The angles CRD and DRB are double the size of the angles CAD and DAB, respectively, and if CAD and DAB are the same, then so are CRD and DRB. Maybe this proof or another proof could have been added.
@MatthewDaly
2 жыл бұрын
The measure of an arc is equal to twice the measure of any inscribed angle that subtends it. Therefore, the arcs subtended by congruent inscribed angles must be congruent. But thinking about the central angles like you did helps with the next "obvious" step that the chords connecting the endpoints of the arcs must also be congruent.
@TomKaren942 жыл бұрын
What is angle chasing?
@mueezadam84383 жыл бұрын
Brilliant presentation
@vortexhuh50463 жыл бұрын
He doesnt say why you can scale it up with a or f and why the triangles are similiar
@atimholt
3 жыл бұрын
We are creating new triangles which we have defined as being scaled versions of given triangles. By the definition of similarity, the new (scaled) triangles are similar to the given triangles.
@ilkmathocam3 жыл бұрын
İspatı kanalımda
@namanchhibbbar22054 жыл бұрын
thats not a mathematical proof
@peterjansen7929
4 жыл бұрын
It leaves out two things, one trivial, the other relevant: 1. The scaling is multiplication with a number, not a length. But this is standard practice. One can always view the drawing as showing not triangles etc. but straight prisms of unit height. A stickler for accuracy can then divide by that unit height at the end and get the correct result, so this is not a serious objection. 2. Not enough evidence is given that the figure shown is really a parallelogram and not a pentagon. Yes, the two sides ab and ba are identical, but the three angles in the middle at the top might not add up to 180°. They do in fact do so, but that should have been made clearer. Follow them back to the first drawing - you will then see that the angle in the middle looks at the diagonal e, as do the two outer angles taken together, though from the opposite side. As opposite angles in a quadrangle of chords add up to 180°, the line at the top is indeed straight and the whole figure is really a parallelogram. For beginners, there should then be another video proving the theorem about opposite angles in a quadrangle of chords.
Пікірлер: 16
@1:53 - you said: "And through angle chasing, we can see that this is a parallelogram." - THAT is the proof. It would have been nice to show an animation of that angle chasing.
subbed!
Nice proofs.
Thanks man
thank you.
♥️♥️♥️♥️♥️♥️♥️♥️
@9:32 - "because angles CAD = DAB, the two arcs that they intercept are equal." - That is true but doesn't seem trivial to me. Is it? I saw that it's true by considering the angles at the center of the circle, R. The angles CRD and DRB are double the size of the angles CAD and DAB, respectively, and if CAD and DAB are the same, then so are CRD and DRB. Maybe this proof or another proof could have been added.
@MatthewDaly
2 жыл бұрын
The measure of an arc is equal to twice the measure of any inscribed angle that subtends it. Therefore, the arcs subtended by congruent inscribed angles must be congruent. But thinking about the central angles like you did helps with the next "obvious" step that the chords connecting the endpoints of the arcs must also be congruent.
What is angle chasing?
Brilliant presentation
He doesnt say why you can scale it up with a or f and why the triangles are similiar
@atimholt
3 жыл бұрын
We are creating new triangles which we have defined as being scaled versions of given triangles. By the definition of similarity, the new (scaled) triangles are similar to the given triangles.
İspatı kanalımda
thats not a mathematical proof
@peterjansen7929
4 жыл бұрын
It leaves out two things, one trivial, the other relevant: 1. The scaling is multiplication with a number, not a length. But this is standard practice. One can always view the drawing as showing not triangles etc. but straight prisms of unit height. A stickler for accuracy can then divide by that unit height at the end and get the correct result, so this is not a serious objection. 2. Not enough evidence is given that the figure shown is really a parallelogram and not a pentagon. Yes, the two sides ab and ba are identical, but the three angles in the middle at the top might not add up to 180°. They do in fact do so, but that should have been made clearer. Follow them back to the first drawing - you will then see that the angle in the middle looks at the diagonal e, as do the two outer angles taken together, though from the opposite side. As opposite angles in a quadrangle of chords add up to 180°, the line at the top is indeed straight and the whole figure is really a parallelogram. For beginners, there should then be another video proving the theorem about opposite angles in a quadrangle of chords.