The figure below shows circle with center o and regular hexagon abcdef constructed inscribed in a circle. which of the following steps will prove that triangle fbd is equilateral?

As mentions in the explanation steps

Step-by-step explanation:

In the given figure hexagonal ABCDEF is a regular hexagonal, therefore each interior angles and sides of the hexagonal are same.

Now, the following steps are  helpful to prove that the triangle FBD is equilateral.

(1). Join the the three pints (pint F, pint B, pint D ) with the help of line segments and formed a triangle FBD.

(2). In ΔFAB, ΔBCD, ΔDEF two sides of each triangle and included angle are same( because two sides of each triangle and included angle must be the sides and interior angle of the given regular hexagon ABCDEF).  So ΔFAB, ΔBCD and  ΔDEF are congruence to each other by SAS postulate.

(3). By corresponding part of congruence triangle we say that line segment FB, line segment BD and line segment DF are same.

(4). Hence ΔFBD is an equilateral triangle, because all sides are same (from step -3).

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