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Consider the square ABCD whose diagonals, AC and BD, meet at X.AB is parallel to DC and AC intercepts them. Therefore <BAX = <DCX.
AB is parallel to DC and BD intercepts them. Therefore <ABX = <CDX.
AB = CD.
Therefore triangle ABX is congruent to triangle CDX (SAS).
So AX = XC ie X is the midpoint of AC and BX = XB ie X is the midpoint of BD.
ie the diagonals bisect each other.
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Which quadrilaterals have diagonals that bisect each other perpendicularly?
squares
In a square to the diagonals bisect each other?
The diagonals of a square bisect each other at 90 degrees
Do the diagonals of a rhombus bisect each other?
Yes. Because the diagonals are perpendicular to each other and intersect at their midpoints, they bisect each other.
Are the diagonals of a trapezoid bisectors?
No, the diagonals of a trapezoid do not necessarily bisect each other. Only in an isosceles trapezoid, where the two non-parallel sides are congruent, will the diagonals bisect each other. In a general trapezoid, the diagonals do not bisect each other.
What can have no right angles and diagonals do not bisect each other?
A circle!! * * * * * Wrong: the diagonals of a circle DO bisect each other. A triangle is a possible answer.
