In a regular hexagon, show that opposite sides are parallel.
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)
∠EFA=∠BCD
∴ΔEFA≅ΔBCD
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.