0
Why do you think that diagonals bisect each other for proving that a quadrilateral is a parallelogram?
Wiki User
∙ 12y ago
The diagonals divide the quadrilateral into four sections. You can then use the bisection to prove that opposite triangles are congruent (SAS). That can then enable you to show that the alternate angles at the ends of the diagonal are equal and that shows one pair of sides is parallel. Repeat the process with the other pair of triangles to show that the second pair of sides is parallel. A quadrilateral with two pairs of parallel lines is a parallelogram.
Wiki User
∙ 12y ago
Add your answer:
Earn +20 pts
The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
False
True or false the diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.
What shapes have diagonals that bisect each other?
A quadrilateral is a parallelogram if and only if its diagonals bisect each other (this should be in any geometry book)
Conditions which guarantee that a quadrilateral is a parallelogram?
Theorem A: A quadrilateral is a parallelogram if its opposite sides are congruent. Theorem B: A quadrilateral is a parallelogram if a pair of opposite sides is parallel and congruent. Theorem C: A quadrilateral is a parallelogram if its diagonals bisect each other. Theorem D: A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.
Do diagonals of a parallelogram bisect each other?
No.
If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram.?
True
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
If the diagonals of a quadrilateral ... each other then the quadrilateral is a parallelogram?
The missing word is "bisect".
A quadrilateral is parallelogram if its diagonals bisect eavh other?
True
If the diagonals of a quadrilateral bisect each other then what quadrilateral must be a parallelogram?
diagonals.
The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
False
The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram.?
false
Is it true that The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
no
True or false the diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.
It is possible for diagonals of a quadrilateral to bisect each other without being a parallelogram?
no
What quadrilateral can have no right angles and diagonals bisect each other?
Parallelogram and rhombus.
