Question

Why isn't the answer parallelogram?

(I am aware a rhombus is a type of parallelogram). Can someone please simply explain? Thank you! I have an exam soon.

Oh yeah: Slope of CD is 0 and Slope of AD is 4/3

Answer 1

`ABCD` is a rhombus.

Explanation:

You have to prove that the diagonals cut at right angles. Then it is a rhombus.

Let the point of intersection of the diagonals be `O`

The height is `=4`

We have

`AB=BC=CD=DA=5`

Diagonal, `AC=sqrt(8^2+4^2)=sqrt80`

So,

`AO=sqrt80/2=sqrt20`

Diagonal, `BD=sqrt(4^2+2^2)=sqrt20`

`BO=sqrt20/2=sqrt5`

So,

In the triangle `AOB`

`AO=sqrt20`

`BO=sqrt5`

and `AB=5`

`AO^2+BO^2=20+5=25=AB^2`

Therefore,

the triangle `AOB` is right triangle ( inverse theorem of Pythagoras)

So, `ABCD` is a rhombus.