DirectX backwards compatibility

[#1]

My son has a Dell OptiPlex 755 computer running Windows XP. XP runs DirectX 9. He wants to upgrade the pc graphics so he can run some computer games on it. The pc has a spare PCIe slot so we could fit a video card in it, but it is difficult getting something new that states it will work with DirectX 9. They all quote DirectX 11.
Is something designed to work with DirectX 11, backward compatible with DirectX 9?
Thanks for any help

[#2]

Windows contains full versions of previous DirectX distributions and graphics cards are fully backwards compatible.

[#3]

DX11 is backwards compatible with DX9, but the DX9 files are not installed by default with DX11 with windows 7/8 if he upgrades.  Usually its DX9 that is the problem, if he gets issues with games not installing as there are missing dlls from DX9
So as a gamer he will have to keep the latest DX9 installer handy for windows reinstall
http://www.microsoft.com/en-gb/download/details.aspx?id=35 Dx9 installer

[#4]

Thanks to both of you.
My son has no plans to upgrade from XP so it is just a case of getting a suitable graphics card that will fit in the pc physically, and will work with XP and DirectX 9
Regards

[#5]

Unfortunately,  it's not going to work.  While DX11 is backwards compatible,  DX 9 is not forward compatible!
The latest and greatest graphics cards are designed to make use of the features of DX 11 and require it to work,  but it's not available for XP.
Edit:
From NVidia,  the latest you could go is a GeForce 500 series card,  which are discontinued.
From AMD,  the Radeon HD 4870 appears to be compatible (assuming the Motherboard supports PCIe x16 gen 2.0)