Question

Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of triangle you have drawn.

Answer 1

Hint: The regular hexagon is the closed shape with 6 sides and 6 vertices and all the sides are equal. Therefore, all the angles between them are equal. To solve this problem, we need to connect any three vertices of the regular hexagon to form a triangle. When any two sides of the triangle are equal then the triangle is called an isosceles triangle. When all the sides are equal then the triangle is called an equilateral triangle.

Complete step-by-step answer:
First, we need to draw the regular hexagon.
A regular hexagon is the closed shape with six equal sides.
It can be drawn as follows,

Let's name all the vertices from A to F.
As we can see that all the sides of the hexagon are equal and all the angles are also equal.
We can write it as,
$AB=BC=CD=DE=EF=FA.....................(i)$
Now, we have been asked to connect three of its vertices and use this to draw a triangle.
So, let's connect AC and the triangle formed is $\Delta ABC$ .
It is shown as follows,

The shaded is the triangle formed.
From equation (i) we can see that,
$AB=BC\ne AC................(ii)$
When two sides of the triangle are equal and not equal to the third side the triangle is called an isosceles triangle.
Therefore, the type of the triangle drawn is an isosceles triangle.


Note: We can connect any three vertices. So, if we connect AE, AC, and CE then by symmetry we will get an equilateral triangle, as all the sides of the triangle are equal. It is shown as follows,

Therefore, there are two correct options for this problem. We need to make sure that all the points of the triangle are the vertices of the regular hexagon.