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How to Prove that a Quadrilateral Is a Square

There are four methods that you can use to prove that a quadrilateral is a square. In the last three of these methods, you first have to prove (or be given) that the quadrilateral is a rectangle, rhombus, or both:

  • If a quadrilateral has four congruent sides and four right angles, then it’s a square (reverse of the square definition).

  • If two consecutive sides of a rectangle are congruent, then it’s a square (neither the reverse of the definition nor the converse of a property).

  • If a rhombus contains a right angle, then it’s a square (neither the reverse of the definition nor the converse of a property).

  • If a quadrilateral is both a rectangle and a rhombus, then it’s a square (neither the reverse of the definition nor the converse of a property).

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