Question

In the figure, ABCDEF is a regular hexagon. △ BDF is drawn by joining the

alternate vertices. Show that △ BDF is equilateral

Answer 1

Explanation:

Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.

Proof

AB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon

∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon

ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence

FB ≅ BD ≅ DF . . . . CPCTC

ΔBDF is equilateral . . . . definition of equilateral triangle