0
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.
What else can I help you with?
Which quadrilaterals have diagonals that bisect each other perpendicularly?
squares
What quadrilaterals have diagonals that do not bisect each other?
Quadrilaterals that have diagonals which do not bisect each other include general parallelograms, trapezoids (especially isosceles trapezoids), and irregular quadrilaterals. In these shapes, the diagonals may intersect at a point but do not split each other into equal halves. This differentiates them from special cases like rectangles and squares, where the diagonals do bisect each other.
Which quadrilaterals have diagonals that are perpendicular each other?
Quadrilaterals with diagonals that are perpendicular to each other include rhombuses, squares, and kites. In a rhombus and a square, the diagonals bisect each other at right angles. In a kite, the diagonals intersect at right angles but do not necessarily bisect each other. These properties are characteristic of these specific types of quadrilaterals.
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.
Which quadrilaterals have diagonals that bisect each other perpendicularly?
squares
What quadrilaterals have diagonals that do not bisect each other?
Quadrilaterals that have diagonals which do not bisect each other include general parallelograms, trapezoids (especially isosceles trapezoids), and irregular quadrilaterals. In these shapes, the diagonals may intersect at a point but do not split each other into equal halves. This differentiates them from special cases like rectangles and squares, where the diagonals do bisect each other.
Do the diagonals of a parrallelogram bisect each other?
Yes, the diagonals of a parallelogram bisect each other.
Which quadrilaterals have diagonals that are perpendicular each other?
Quadrilaterals with diagonals that are perpendicular to each other include rhombuses, squares, and kites. In a rhombus and a square, the diagonals bisect each other at right angles. In a kite, the diagonals intersect at right angles but do not necessarily bisect each other. These properties are characteristic of these specific types of quadrilaterals.
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.
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 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.
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
