Do you discuss the nature of valid proofs, e.g. the diagonals of a parallelogram ABCD: Is the following a valid proof? Am I allowed to specify the midpoint on one diagonal and prove that the other diagonal passes through it and is bisected?
Let v=AB=DC and u=AD=BC, then the diagonals of the parallelogram are AC=u+v and BD=u-v. Let E be the midpoint of BD, i.e. BE=1/2(u-v).
AE=v+1/2(u-v)=1/2(u+v)=1/2 AC. But AE+EC=AC, so AE=EC=1/2 AC.
Hence the diagonals of a parallelogram bisect each other.
i like the drumstick as a pointer...
tzotzo 1 month ago
nicely discussed...
thegreeensky 3 months ago
thank you caption sir.
sanzillajackcat 10 months ago
@38:58 is this there a version of this median 2:1 ratio proof in Euclid's Elements?
samruby82 10 months ago
Do you discuss the nature of valid proofs, e.g. the diagonals of a parallelogram ABCD: Is the following a valid proof? Am I allowed to specify the midpoint on one diagonal and prove that the other diagonal passes through it and is bisected?
Let v=AB=DC and u=AD=BC, then the diagonals of the parallelogram are AC=u+v and BD=u-v. Let E be the midpoint of BD, i.e. BE=1/2(u-v).
AE=v+1/2(u-v)=1/2(u+v)=1/2 AC. But AE+EC=AC, so AE=EC=1/2 AC.
Hence the diagonals of a parallelogram bisect each other.
hugstablebear 1 year ago