[Junior high school mathematics] A right triangle with a special angle (30 degrees, 45 degrees)

The relationship between the sides of a right triangle with degrees is as follows.

Note: Numbers in the figure indicate the multiple relationship between sides.

Namely, the following two conclusions (points)

The key is to prove

A right-angled side is half of a hypotenuse.

The latter (the right-angled side is twice as large as the right-angled side) can be quickly obtained by Pythagorean theorem.

There are two ways to prove it, one is simple and the other is slightly complicated.

Proof 1: Fold to create an equilateral triangle.

Method 2: center line of hypotenuse

Then according to Pythagorean theorem, we can get

As shown in the figure below, find the corresponding side length (letters marked in red) in each special triangle.

Basic exercises 1

Basic exercise 2

BD=6

Ideas:

outdoor training

The idea is as follows: