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Which concept can be used to prove that the diagonals of a parallelogram bisect each other?
Congruent triangles:
Take a parallelogram PQRS.
Draw in the diagonals PR and QS.
Let the point where the diagonals meet be M,
Consider one pair of the parallel sides, PS and QR, say.
Consider angles PSQ and RQS:
As PS and QR are parallel they are equal (Z- or alternate angles).
Now consider angles SPR and QRP:
As PS and QR are parallel they are equal (z- or alternate angles).
As PS and QR are opposite sides of a parallelogram they are equal in length; thus the triangles PMS and RMQ are congruent (Angle-Angle-Side).
As the two triangle are congruent, equivalent sides are equal in length.
Thus QM is the same length as MS and PM is the same length as MR
As QM is the same length as MS and QMS lie on a straight line, M must be the mid point of QS, ie the diagonal PQ bisects the diagonal QS
Similarly PM is the same length as MR and PMR lie on a straight line, thus M must be the mid point of PR, ie the diagonal QS bisects the diagonal PR
Therefore the diagonals of a parallelogram bisect each other.
What else can I help you with?
Do the diagonals of a parallelogram bisect its opposite angles?
Not for every parallelogram. Only for a rhombus (diamond) or square will the diagonals bisect the opposite angles they connect, and diagonals are perpendicular. In rectangles, the diagonals do not bisect the angles and are notperpendicular, but they do bisect each other.
Which quadrilaterals have diagonals that bisects each other?
A quadrilateral whose diagonals bisect each other at right angles is a rhombus. each other at right angles at M. So AB = AD and by the first test above ABCD is a rhombus. 'If the diagonals of a parallelogram are perpendicular, then it is a rhombus
It is possible for diagonals of a quadrilateral to bisect each other without being a parallelogram?
no
If both diagonals of a quadrilateral bisect each other when is the quadrilateral a parallelogram?
always
If the diagonals of a quadrilateral bisect each other then the quadrilateral must be a parallelogram?
true
Do the diagonals of a parrallelogram bisect each other?
Yes, the diagonals of a parallelogram bisect each other.
Does a parallelogram have diagonals bisect each other?
Yes every parallelogram has bisecting diagonals
Do diagonals of a parallelogram bisect each other?
No.
Do the diagonals of a parallelogram bisect its opposite angles?
Not for every parallelogram. Only for a rhombus (diamond) or square will the diagonals bisect the opposite angles they connect, and diagonals are perpendicular. In rectangles, the diagonals do not bisect the angles and are notperpendicular, but they do bisect each other.
The diagonals of a parallelogram must be what?
The diagonals of a parallelogram are congruent (equal in length) and bisect each other.
What is a quadirlateral with diagonals that bisect each other?
A parallelogram.
Does the diagonals of a parallelogram bisect each other?
Yes
In parallelogram the diagonals have the same midpoint?
Yes the diagonals of a parallelogram have the same midpoint since they bisect each other.
Are diagonals of a parallelogram perpendicular?
Only if the parallelogram is in the form of a rhombus will its diagonals bisect each other at right angles
Are the diagonals of a paralelogram bisectors of each other?
The diagonals of a parallelogram will always bisect each other. ■
A quadrilateral is parallelogram if its diagonals bisect eavh other?
True
Do diagonals in a parallelogram bisect each other?
yes
