Extra: right-triangle theorems
In a right-angled triangle with a 30° angle, the side opposite it is half the hypotenuse; and the median to the hypotenuse is half of it too. See both, prove one and use them.
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Guide
This is an extra studio: these two theorems are in the Afghan Grade 8 book. You can understand them with congruent triangles and isosceles triangles.
The 30° theorem: if one acute angle of a right-angled triangle is 30°, the side opposite it is half the hypotenuse. That's because such a triangle is half of an equilateral triangle. The rule only works for 30°, not for any angle.
The median theorem: in a right-angled triangle, the median from the right angle to the hypotenuse is half the hypotenuse. The midpoint of the hypotenuse is the same distance from all three vertices, so a circle centred there passes through all three.