Question

In a regular Hexagon, Prove that pairs of opposite sides are equal!

Answer 1

Answer:

Let's we take LMNOPQ is a regular hexagon.

LMN = OPQ

LMN ≅ OPQ

∴ LM is parallel to OP.

Hence opposite sides of a regular hexagon are parallel.

Answer 2

Answer:

$\huge{\mathcal{\underline{\green{ANSWER}}}}$

Step-by-step explanation:

Given:

ABCDEF is a regular hexagon

To prove :

AB is parallel to ED

Construction:

Join AE, 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.