(524) How to fold an equilateral triangle

   Triangles are taught in the third grade of elementary school in Japan.

正三角形 : equilateral triangle
直角三角形 : right triangle
二等辺三角形 isosceles triangle

  One day, a third-year pupil taught me how to fold an equilateral triangle from a square paper.

1. Fold the paper in half to make a rectangular.

2. Fold the rectangular in half  again, crease it and reopen.

3. Fold the upper right corner diagonally on its horizontal crease to make a right-angled triangle. Next, fold the lower left corner diagonally on its vertical crease as it is shown above.

4. Finally fold the lower right corner diagonally to make a triangle.

5. Turn it over the triangle, it is an equilateral triangle.

小学校で習った言葉「さか上がり」「行ってきます」を英語で言えますか? (Sanrio SMILES)

• 作者: 誠, 守
• 出版社/メーカー: サンリオ
• 発売日: 2017/12/01
• メディア: 単行本

正方形：square

長方形：rectangular

 

Why does the folded  shape become an equilateral triangle?

 

△ABD is a right-angled triangle.

AB : AD = 2 : 1

So, we can know.

∠BAD = 60°　

∠EAB = (90° - 60°) ÷ 2 = 15°

∠FAC = ∠EAG = 15°

Now we can see △AEF.

AE = AF

∠EAF = 90° - 15° - 15° = 60°

Therefore,

△EAB is an equilateral triangle.

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