...to only assert things as fact that were proven to be true, and that only when the speaker knows of and understands the proof. If someone you respect asserts a fact, then it is fine to accept that as evidence, but not proof.

For instance, calamine lotion was asserted to be a good treatment for poison oak for many years. It was "taught" to doctors that this was true. Many people attested to having experienced a benefit from using it. And yet, when put to a clinical test it was found to have no benefit other than placebo effect.

In my personal experience, I was taught that stretching before exercise was important to reduce injury. I passed on that "learning" to my aerobics classes as fact. Turns out that stretching does not reduce injury. Warming up prior to exercise was found to have a small effect, though.

I think people just need to look into things and to be cautious. And maybe geometry should be a mandatory class.