The fact that the shear stress is a maximum at 45 degrees to the loading axis is shown by an equilibrium diagram of a small element of material under load. The best source of these can be found in derivations and descriptions of Mohr's Circle, such as this:
Mohr's Circle
This shows that the shear stress is a maximum when two-theta (sorry I don't know how to write Greek letters on this thing...) is 90 degrees, so theta is 45 degrees.
When a sample of ductile metal such as steel is pulled in a testing machine until it fails, the failure always exhibits a 45 degree 'lip'. In a rod, this failure has a 'cup and cone' appearance because the lip is circular. The 45 degree planes are where the maximum slippage has occurred between the crystals in the material, which is the mode of failure, and of course the slippage occurred along the plane of maximum shear stress. When you are examining wreckage from an aircraft accident, the bits that failed in tension are immediately obvious from these 45 degree features. They tell you the tensile loading direction too!
I hope this helps. Mohr's Circle is the key; hopefully it will be somewhere a few pages ahead in your stepson's textbook, but if not the internet has many more references than this one.
By the way, strain gauges work very well in compression.
