Question

PLEASE HELP The figure below shows circle with center O and regular hexagon ABCDEF constructed inscribed in a circle.Which of the following steps will help prove that triangle FBD is equilateral? IS IT Prove that DA, EF, and CB are parallel or Prove that triangles BDC, DFE, and BFA are congruent

Answer 1

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.

Answer 2

I hope this helps you