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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.
Which quadrilaterals have the property that the diagonals bisect each other?
Square, rhombus and a kite have diagonals that bisect each other at 90 degrees
Which quadrilaterals have diagonals that bisect each other perpendicularly?
squares
Why do diagonals on a kite bisect each other?
name 4 diagonals that bisect each other
Do the diagonals of a parrallelogram bisect each other?
Yes, the diagonals of a parallelogram bisect each other.
Do diagonals of a rectangle bisect each other?
The diagonals of a square (which always bisect each other) are the same length.
In a square to the diagonals bisect each other?
The diagonals of a square bisect each other at 90 degrees
Does a kite have diagonals that bisect each other?
Yes the diagonals of a kite bisect each other at 90 degrees.
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.
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.
Does an isosceles trapezoid have diagonals that bisect each other?
An isosceles trapezoid, or any trapezoid, does not have diagonals that 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.
Which quadrilaterals have the property that the diagonals bisect each other?
Square, rhombus and a kite have diagonals that bisect each other at 90 degrees
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.
