Question

In regular hexagon $ABCDEF$, prove that $\overline{AB}\parallel \overline{DE}$.

Answer 1

$ABCDEF$ is a regular hexagon.

Join $AE$ and $BD$

In $△EFA$ and $△BCD$

$\Rightarrow$ $EF=CD$ [ Sides of regular hexagon are equal ]

$\Rightarrow$ $AF=BC$ [ Sides of regular hexagon are equal ]

$\Rightarrow$ $\angle EFA=\angle BCD$

$\therefore$ $△EFA\cong △BCD$

$\Rightarrow$ $AE=BD$ [ Corresponding sides of congruent triangles ]

$\Rightarrow$ $AB=ED$ [ Sides of regular hexagon ]

$\therefore$ $AB\parallel ED$ --- Hence proved.