The plane angle of dihedral angle A-BD-C is: take the midpoint of BD as O and connect AO and CO, then ∠AOC is the required dihedral angle;

According to AB=AD =a. BD = √2a, calculate ao =1/2bd =1/2× √ 2a; Similarly, CO = 1/2 BD = AO can be calculated.

Then ∠ AOC = 90 is a right angle.

Supplementary notes AB = AD = a, BD = √2a. Using Pythagorean theorem, it is shown that triangle ABD is an isosceles right triangle, and the height of hypotenuse of isosceles right triangle is higher than half of hypotenuse. This is a basic theorem of isosceles right triangle.

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