Prove the first half theorem, when Rt△ABC, ∠ ACB = 90, ∠ A = 30, then BC=AB/2.

Take the midpoint d of AB and connect CD. According to the hypotenuse midline theorem of right triangle, we can know that CD=BD and BCD are equilateral triangles (an isosceles triangle with an angle of 60 is an equilateral triangle).

Projection theorem, also known as Euclid theorem: in a right triangle, the height on the hypotenuse is the median of the projection of two right-angled sides on the hypotenuse, and each right-angled side is the ratio of the median of the projection of this right-angled side on the hypotenuse to the hypotenuse. It is an important theorem of mathematical graphic calculation.

In a right triangle, if there is an acute angle equal to 30, then the right side it faces is equal to half of the hypotenuse. In a right triangle, if there is a right-angled side equal to half of the hypotenuse, then the acute angle of this right-angled side is equal to 30. There are many ways to prove it. The following is a simple geometric proof.