Marking schedule from 2013

Mathematics Level 1 1.6 Geometric reasoning
1

Hello I have just done the 2013 paper and i was just going through the marking schedule. This is what I wrote for for 3 b. (iii). 2013

So first of all i proved that the opposite angles of the quadrilateral HXKJ are equal.

Let angle JHX be x and angle HXK be y

Co -interior angles on parallel lines add up to 180.
∴ ∠HXK = 180-y
Angles on a straight line add up to 180
∴∠XKJ = 180-(180-y)
=y
Opposite angles are equal
In the same way we can prove that ∠HJK is y

Then i said that “we know that the quadrilateral HXKJ is a rhombus as we know that the opposite angles of a rhombus are equal”.

But in the answers it says

Since HJK = HXK = 120°, and JHX =
JKX = 60°, we have 2 pairs of cointerior
angles:
JKX and HXK show that HX // JK.
Hence HJKX is a parallelogram.
Also, since HX = XK (radii) and
opposite sides of a parallelogram are
equal,
HX = JK and XK = HJ, and hence
HJKX is a rhombus

This is an E answer. So my question is, that if you were marking the test and you saw my answer and compared it to the marking schedule what would you give it?

Its question 3 (iii) from the 2013 geometric paper

2

Showing that opposite angles are equal is not sufficient to prove that the figure is a rhombus.
For example rectangles, squares, parallelograms also have opposite angles equal.

In order for the quadrilateral to be a rhombus, you must show that each pair of opposite sides are equal in length and parallel.