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How many equilateral triangles are there in a regular hexagon?
A regular hexagon is a polygon with 6 equal sides and 6 equal angles.
Answer: There are 6 equilateral triangles in a regular hexagon.
Let's look into the structure of a regular hexagon with all the end-to-end vertices connected.
An equilateral triangle is a regular polygon with 3 equal sides with each angle equal to 60 degrees.
We know that the sum of interior angles of a hexagon is 720°
Thus, each interior angle of a hexagon measures 120°(since, 720/6 = 120)
When the lines are connected using two opposite vertices, the internal angles are bisected, hence, each angle is 60° in measure.
The angle at the center of the hexagon is 360° which is being divided into 6 equal parts.
Thus, the value of each angle at the center is equal to 60°.
Hence, we see that all three angles of the 6 triangles formed in the given hexagon are equal to 60°.
This proves that there are 6 equilateral triangles.
We can thus form 6 equilateral triangles by connecting the opposite vertices of a regular hexagon.
Hence, there are 6 equilateral triangles in a regular hexagon.