Made from Geometry

Geometry Level 3

A Quadrilateral with equal diagonals must be a

None of these choices Rectangle Isosceles Trapezoid Square

Vishal Yadav by Vishal Yadav , 20, India

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1 solution

Vishal Yadav
Dec 22, 2015

THE ANSWER.

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But rectangles have the diagonals of the same length. In addition, they are quadrilaterals. So, why is a wrong answer and the square as well?

Franderly Acosta Valdez - 5 years, 5 months ago

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Note that is says must be a . So, the fact that rectangles have equal diagonals, means that the answer is not a square. The fact that rhombuses have equal diagonals, means that the answer is not a rectangle.

In fact, as Vishal is pointing out, there is no "proper" classification of such a quadrilateral. We can take any 2 line segments of equal length, and connect up their 4 points (assuming that the side lengths do not cross). In fact, there is no guarantee that such a quadrilateral must be convex.

Calvin Lin Staff - 5 years, 5 months ago

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