1. To make it easier to cut the tile diagonally, expand the frame of the image, so that there is "spare" space all around it.

2. Click on the Select tool and choose "Freehand Selection". 

3. The selection type must be

Point to point

Mode is Replace

Feather = 0

Smoothing = 0

Anti-alias is off

4. Using the Freehand selection tool you then click in the empty space (a) up and left of the top left corner. This will create a starting point right in the corner of the tile. (Click and then release then mouse button).

5. Then position your mouse cursor (with the rope trailing a line) in the empty space at the lower right of the tile (b). Click once.

6. Now position the mouse cursor (still with the rope trailing a line) in the top right empty space and click (c).

7. Finally move back to the top left corner and double-click (d).

The top right half of the image will be surrounded by a flashing selection line.

8. Now go to the Layers Menu and select

Promote Background Layer.

9. Press the delete button and the selected part of the image will disappear. This portion is now transparent.

We can now either fill this with color and texture it OR we can slide in another image.

Before proceeding, ensure that the flashing selection line is still there. (If it isn't you might be able to get it back by pressing CTL-Z or Edit-Undo).

10. Firstly, let's fill the space with a colour selected from the image.

Use the eye dropper tool and pass it over the image until you find a colour you want to fill the upper triangle with. When you see the colour you want, just click the left mouse button to select the colour.

11. Then select the paint bucket tool, move your mouse into the empty triangle and click the left mouse button.

12. After filling the area with your selected colour, and still with the flashing selection lines around this area, go to the Effects Menu.

Select Texture Effects, then Weave (or whatever texture you want to use).

13. Your tile should look something like this!

Whilst you have the right tile selected, press CTL-C to copy it.

Press CTL-V and the image previously copied to the clipboard will be pasted over this tile. They should fit perfectly together with no gaps.

This is a bit trickier as you have to find the exact centre of the tile. You can do this by looking at the cursor position shown and the bottom right of your screen.

See where it has (x:250 y:250) -- Image: 500 x 500 x 16 million

The size of my image is 500 pixels square, therefore the exact centre is when my cursor is at co-ordinates (x:250 y:250)

When you get the right position, click the mouse once.

It's best to start with empty space around the outside of the image so that you can now move up to the top right corner, click, move to the top left corner, click and move back close to the centre (doesn't have to be exact) and double-click. This will complete the "circuit".

Do the usual "Promote Background layer" and delete.

Then you will be able to fill the empty space (still surrounded by flashing selection lines) with a colour and apply a texture.

Open all 3 images.

Click on the frame of Image 1 and press CTL-V to paste the copied part of Image 2 over the top.

Click on the frame of Image 1 and press CTL-V to paste the copied part of Image 3 over the top.