Question

State true or false:

In a regular hexagon, the opposite sides are parallel.

• A. True
• B. False

Answer 1

The correct option is A True

Given: $ABCDEF$ is a regular hexagon.
Join $AE,BD$
Consider $DEFA$ and $DBCD$
$EF=CD$ (sides of the regular hexagon)
$AF=BC$ (sides of the regular hexagon)
$\angle EFA=\angle BCD$
$△EFA\cong △BCD$
$AE=BD$(Corresponding sides of congruent triangles)
$AB=ED$ (sides of the regular hexagon)
$AB$ is parallel to $ED$.
Hence opposite sides of a regular hexagon are parallel.