Question

Arlan states, "If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a rhombus." Decide if his statement is true or false.

A. True
B. False

Answer 1

@Catlover5925

Answer 2

@extremearianna

Answer 3

Properties of Parallelograms
In a parallelogram,
1. The parallel sides are parallel by definition.
2. The opposite sides are congruent.
3. The opposite angles are congruent.
4. The diagonals bisect each other.
5. Any pair of consecutive angles are supplementary.

Answer 4

So it's true than since a rhombus can be put into diagonals? @perl

Answer 5

so a rectangle with unequal adjacent sides satisfies the hypotheses, but it not a rhombus

Answer 6

not quite

Answer 7

I'm confused, so it's false?

Answer 8

if the diagonals of a quadrilateral bisect each other, does it need to be a rhombus?

Answer 9

No it does not. So it's false! :)

Answer 10

the statement is saying

if the diagonals of a quadrilateral bisect each other, then the figure needs to be a rhombus.

But there are counterexamples to this

Answer 11

right

Answer 12

Thank you!