Question

state whether the statement is is true or false. equilateral quadrilateral must be a regular polygon​

Answer 1

Equilateral quadrilateral must be a regular polygon - False

• An equilateral quadrilateral refers to a figure having each side equal i.e. a rhombus.
• In rhombus, all sides are equal and diagonals bisect each other at right angles.
• While in a regular polygon, all angles are also equal (equiangular) in addition to being equilateral.  
• Since a rhombus is not equiangular, the given statement doesn't hold true.

Answer 2

Given  : A statement

Equilateral quadrilateral must be a regular polygon.​

To Find : statement is true or false

Solution:

a regular polygon.​ is a polygon whose all sides and all angles are equal

Equilateral Triangle is a regular polygon of 3 sides

But Equilateral quadrilateral  is NOT necessarily a regular polygon of 4 sides .

Square is a regular polygon of 4 sides

Square is a quadrilateral which is a regular polygon.​

Equilateral quadrilateral means all four sides are equal.

and there is no information about angles being Equal or not

Like a  Rhombus has All Sides Equal  is an Equilateral quadrilateral but not a regular polygon

Hence Equilateral quadrilateral must be a regular polygon.​ is FALSE

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