MHB Quadrilaterals with diagonals that don't bisect one another

[teacher ARTHUR]

i have read this question from a book:

WHICH OF THE FOLLOWING QUADRILATERALS HAS DIAGONALS THAT DO NOT BISECT EACH OTHER?
A. SQUARE
B. RECTANGLE
C. RHOMBUS
D. TRAPEZOID

my answer is none of the given choices...
for irregular quadrilaterals may be... as concave polygon

I'M looking for forward for additional explanation, thank you...

 

[MarkFL]

What does it mean to bisect a line segment?

 

[teacher ARTHUR]

diagonals form by two opposite vertices. Example given parallelogram ABCD then the diagonals are line segment AC and BD.

 

[MarkFL]

diagonals form by two opposite vertices. Example given parallelogram ABCD then the diagonals are line segment AC and BD.

That's true, but I was asking about bisection of a line segment. :)

 

[Furlo]

Since the question is about diagonals bisecting each other, which effectively means they cut each other in half, the correct answer to the question is D. Trapezoid, since the others fall into the category of the parallelogram, whose diagonals always bisect.

When you said that none of the above was correct, I think what you were referring to was intersecting diagonals, in which case you would be correct. All 4 answers are convex quadrilaterals, so their diagonals will intersect. In concave ones (a boomerang for example), they do no intersect.

Hope this helped and it's not too late :)

 

[phymat]

If, for example, the word bisect is used in a different context, then it only means to divide in two parts. But in Geometry, it means to divide in two equal parts. Word bi means two and word sect means to cut. The answer therefore, as already posted above, is Trapezoid.

 

[IHateFactorial]

That's true, but I was asking about bisection of a line segment. :)

I believe the bisecting bit means that, given a quadrilateral ABCD, where AD and BC are the diagonals, say they intersect at point M; they bisect is AM = MD and BM = MD... Unless you already knew that.

 

[MarkFL]

I believe the bisecting bit means that, given a quadrilateral ABCD, where AD and BC are the diagonals, say they intersect at point M; they bisect is AM = MD and BM = MD... Unless you already knew that.

I was asking to see if the OP knew, in an effort to guide them to a solution. :)