Answer with explanation:
Regular hexagon A B C DEF is inscribed in a circle having center O.The meaning of regular Hexagon is that all it's interior angle as well as Exterior angle are equal as well as all it's sides are equal.
We have to prove that, ΔFBD is equilateral.
→To prove this we will prove that, triangles B DC, D FE, and B FA are congruent.
Proof:
In ΔB DC and Δ D FE
→ BC=DE
→ CD=EF
→∠BCD=∠DEF
Sides as well as Interior angles of regular Hexagon are congruent.
→→ΔB DC ≅ Δ D FE-----[S AS]
Similarly,→Δ DFE, ≅ ΔBFA -----[S AS]
Also, →ΔB DC ≅ Δ B FA -----[S AS]
Therefore these three triangles are congruent to One Another.
→Which gives, BF=FD=DB---------[Corresponding Part of Congruent Triangles Abbreviated as C PCT]
→Showing Δ F B D is equilateral.
