Link between bcg and ansoff

Hi,
Here is my version of combining the two but not sure if I my approach correct:

BCG (position of products within portfolio):
Star – High Growth; High Share; – new product which gain market recognition
Cash Cow – Low Growth; High Share; – fallen star company enjoy low costs and high mg
Dog – Low Growth; Low Share; – products at the end of their life
Problem Child – High Growth; Low Share; – New products

Ansoff (growth strategy):
Diversification – New Product; New Market
Product development – New Product; Existing Market
Penetration – Existing Product; Existing Market
Market development – Existing Product; New Market

BCG and Ansoff together:
Diversification – product is not in your portfolio and market is different to yours;
Product development – problem child
Penetration – reposition the product (possibly cash cow or dog)
Mk development – could be all due to different market preferences;

There is no need to penetrate with Stars as market is already growing alongside with share. You apply Ansoff when you are looking for expansion/growing strategies.

Regards,