Is a quadrilateral a square?
1) 3 sides are equal
2) 3 angles are 90 degrees.
Think of it this way:
Stmnt 1. Even if all 4 sides are equal, it still may not be a square. It may be a rhombus (angles are not 90 degrees). Clearly not sufficient.
Stmnt 2. 3 angles 90 degrees means the fourth angle has to be 90 degrees too (since the sum of all interior angles of a quadrilateral is 360 degrees). But if a quadrilateral has all four angles 90, does it mean it is a square? No. It could be a rectangle. Only opposite sides are equal in length in a rectangle. Not sufficient.
Using both statements: The quadrilateral must have all four angles 90 degrees. Since 3 sides are equal, the fourth one must be equal to these 3 since the pair of opposite sides must be equal if all four angles are 90 degrees. Hence, the quadrilateral must be a square.
Hi, I need some clarity on quadrilaterals concepts/rules.
I would suggest you to check out the Veritas
Geometry book. It covers lines, angles, triangles, quadrilaterals, circles, 3 D figures, co-ordinate ... pretty much everything you might see on GMAT.
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