If all the 4 sides of a quadrilateral are equal but only 3 of its angles are equal. Is it a square?

I am wondering if all the four sides are equal and 3 of the 4 interior angles are equal, doesn't it necessarily mean that the 4th angle would also be equal to the rest of the three? Hard time visualizing it..


1 Answer 1


If a quadrilateral has its sides equal, it is a rhombus. And if a rhombus has three angles equal, it is a square.

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    $\begingroup$ The opposite angles of a rhombus are equal. So when three are equal to each other then all four are equal to each other. $\endgroup$ Commented Aug 7, 2015 at 12:21
  • $\begingroup$ That makes sense. Since Opposite angles are equal is so since 3 are equal the fourth one would also be equal. $\endgroup$
    – Jason
    Commented Aug 7, 2015 at 12:27
  • $\begingroup$ @Jason : note that this is true only if the quadrilateral is not crossed (self intersecting), You can have a self intersecting quadrilateral with 4 sides and 4 angles equals, and it's obviously not a square $\endgroup$
    – Tryss
    Commented Aug 7, 2015 at 12:36
  • $\begingroup$ Yes, that's true. $\endgroup$
    – Jason
    Commented Aug 7, 2015 at 12:43

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