Question

Kevin draws a figure that has four sides. All sides have the same length. His figure has no right angles. What figure does Kevin draw?

Answer 1

Rhombus

Explanation:

A quadrilateral with all sides of the same length is rhombus.

The proof:
Given a quadrilateral `ABCD` with `AB=BC=CD=AD`.

Consider triangles `Delta ABC` and `Delta ADC`.
They are congruent by three sides. Therefore, angles `/_BAC` and `/_ACD` are congruent. Hence, `AB` `||` `CD`.

Analogously, `AD` `||` `BC`.
Therefore, `ABCD` is a parallelogram. Since all sides of this parallelogram are congruent, it's a rhombus.