Formulate and prove the properties of the angles of a right triangle.

Right-angled triangle – a triangle with a right angle, which is 90º, and two acute angles.
1) In a right-angled triangle, the sum of two acute angles always equals 90º, since the sum of all the angles of a triangle is 180º, which means: 90º + aº + bº = 180º.
2) The side opposite the 30º angle is half the hypotenuse.
3) In a right-angled triangle, the sides and angles are connected with each other using: sin, cos, tg, ctg.
4) If the leg is half the hypotenuse, then the opposite angle is 30º.