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Is a rectangle always a rhombus? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Classify quadrilaterals I

Full solution

Q. Is a rectangle always a rhombus?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Understand Definitions: Step $1$ : Understand the definitions of a rectangle and a rhombus. $\newline$ A rectangle is a quadrilateral with all angles equal to $90$ degrees. A rhombus is a quadrilateral where all sides have equal length.
Compare Properties: Step $2$ : Compare the properties. $\newline$ For a rectangle to be a rhombus, all its sides must be of equal length. However, a rectangle typically has opposite sides equal, not necessarily all four sides.
Analyze with Example: Step $3$ : Analyze with an example. $\newline$ Consider a rectangle with sides $4\,\text{cm}$ and $6\,\text{cm}$ . All angles are $90$ degrees, but not all sides are equal. This rectangle is not a rhombus.
Conclude Based on Properties: Step $4$ : Conclude based on properties. $\newline$ Since a rectangle does not require all sides to be equal, but a rhombus does, not all rectangles are rhombuses.

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