Question

In a regular hexagon, show that opposite sides are parallel.

Answer 1

Given: $ABCDEF$ is a regular hexagon.

RTP: $AB$ is parallel to $ED$

Construction: Join $AE$ and $BD$

Proof: Consider $DEFA$ and $DBCD$

$EF=CD$ (sides of the regular hexagon)

$AF=BC$ (sides of the regular hexagon)

$\angle EFA=\angle BCD$

$\therefore \Delta EFA\cong \Delta BCD$

$AE=BD$ (Corresponding sides of congruent triangles)

$AB=ED$ (sides of the regular hexagon)

$\therefore AB$ is parallel to $ED$.

Hence, opposite sides of a regular hexagon are parallel.