In the following problem Khan claims that the upper angle is $\theta$ since the angle on the bottom right is $90°-\theta$ and it is a right triangle. However I don't see any proof that the striped line is perpendicular to the base of the pyramid to call it such.
Also he claims that the triangle in blue with side $h$ is also a right triangle by the black line hitting the top of the water. But I don't see any proof of this either.
He also claims the diagonal right side of the pyramid is $180-72$, but how can we know that the pyramid isn't asymmetric?
Am I right to say that in simple geometry problems such as these you just have to "assume" right triangles and symmetry without proof for simplicity sake? Maybe I am being stupid here.