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Q: What type of figure must a quadrilateral be if its diagonals are perpendicular bisectors of each other and are congruent?

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A square.

In general, no, they are not.

square

It can be :- 1- a parallelogram 2- Square if diagonals are perpendicular and congruent 3- Rectangle if diagonals are congruent 4- Rhombus if diagonals are perpendicular

It could be a square, but consider the following congruent & perpendicular 'diagonals of a quadrilateral (you will have to connect the endpoints of the diagonals, yourself, as it cannot be drawn in text): . _|___ . | . | . | If the two diagonals, also bisect each other, then it's a square, otherwise it is not.

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If the diagonals are congruent and are perpendicular bisectors of each other then the parallelogram is a square. If the diagonals are not congruent but are perpendicular bisectors of each other then the figure would be a rhombus.

A square.

The quadrilateral that must have diagonals that are congruent and perpendicular is the square. This is because its diagonals form a right angle at its center.

In general, no, they are not.

square

It can be :- 1- a parallelogram 2- Square if diagonals are perpendicular and congruent 3- Rectangle if diagonals are congruent 4- Rhombus if diagonals are perpendicular

square

It could be a square, but consider the following congruent & perpendicular 'diagonals of a quadrilateral (you will have to connect the endpoints of the diagonals, yourself, as it cannot be drawn in text): . _|___ . | . | . | If the two diagonals, also bisect each other, then it's a square, otherwise it is not.

True, the diagonals of a rhombus are perpendicular bisectors of one another.

Rectangle: A quadrilateral with 4 right angles, diagonals congruent/bisecting, and opposite sides congruent, BUT ADJACENT SIDES ARE NOT CONGRUENT. Rhobus: A quadrilateral with opposite congruent angles, but adjacent angles are Not congruent, perpendicular bisecting diagonals and 4 congruent sides. Square: A quadrilateral that is a rectangle and a square with 4 right angles, diagonals congruet/bisecting that ar perpendicular, and opposites sides congruent.

Not necessarily - the diagonals of a rhombus bisect each other (they are perpendicular bisectors of each other), but are not equal.

No, they are just bisectors. The angle between them is not (usually) the 90o required to be perpendicular.

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