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You could prove this by congruent triangles, but here are two simpler arguments:
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Since a square is a rhombus, and the diagonals of a rhombus are perpendicular bisectors of each other, then the diagonals of a square must be perpendicular bisectors of each other
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A square has four-fold rotational symmetry - as you rotate it around the point where the diagonals cross, there are four positions in which it looks the same. This means that the four angles at the centre must be equal. They will each measure 360/4 = 90 degrees, so the diagonals are perpendicular. Also. the four segments joining the centre to a vertex are all equal, so the diagonals bisect each other.
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The diagonals of a square are perpendicular bisectors of each other?
Yes
How are the diagonals of a square?
The diagonals of a square are congruent, bisect each other, perpendicular, and either diagonal's length is sqrt(2) times any side length.
What quadrilaterals Have diangles that are perpendicular to each other?
A square, a rhombus and a kite are three examples of quadrilaterals that have perpendicular diagonals that intersect each other at right angles.
Do the diagonals of a parallelogram bisect each other at a right angle?
Only for a square or rhombus (diamond shape). The diagonals of a rectangle bisect each other, but are not perpendicular and do not bisect the opposite angles they join.
What is quadrilateral whose diagonals are perpendicular to each other but unequal?
It is a kite or a rhombus both of which have unequal diagonals that are perpendicular to each other creating right angles.
What kind of parellogram is it If the diagonals of a parallelogram are congruent and are perpendicular bisectors of each other?
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.
The diagonals of a square are perpendicular bisectors of each other?
Yes
Are the diagonals of a square perpendicular bisectors to each other?
Yes
What type of parallelogram always has diagonals that are congruent and are perpendicular bisectors of each other?
square
Diagonals of a rhombus are?
Perpendicular bisectors of each other.
Are diagonals congruent if they bisect each other?
Not necessarily - the diagonals of a rhombus bisect each other (they are perpendicular bisectors of each other), but are not equal.
In a parallelogram the diagonals are perpendicular bisectors of each other What kind of parallelogram must the figure be?
It is a rhombus
Are a trapeziums diagonals perpendicular?
No but the diagonals of a square, rhombus and a kite are perpendicular to each other
What type of figure must a quadrilateral be if its diagonals are perpendicular bisectors of each other and are congruent?
It is a square because its diagonals are equal in length and they bisect each other at right angles which is 90 degrees The diagonals of a rhombus are not equal in length but they meet at right angles.
What is the name of the quadrilateral that are perpendicular and bisect each other?
If you are talking about the diagonals of a quadrilateral, the only quadrilateral that have diagonals that are perpendicular and bisect each other is a square, because a rectangle has bisecting diagonals, while a rhombus has perpendicular diagonals. And a square fits in both of these categories.
Are the diagonals perpendicular?
Not always but they are perpendicular in a square, a rhombus and a kite in that the diagonals intersect each other at 90 degrees
Do the diagonals on a square perpendicular to each other?
Yes they do.
