How to replace .php files in main theme with child ones

Before I started I’ve been though more pages on how to do this than I care to mention and I must just be not getting it however I have changes I’ve made to two files in my themes page

header-extensions.php
footer-extensions.php

Now I wish to get my child theme function to replace main themes versions with mine. I’ve tried wrapping them in an if(‘function_exists to test for the function theme has to load these amongst others however I just get the page breaking. I understand the error about declarations not being the same name surly for the theme to use them they have to be.

Am I really missing the point or should this not be fairly simple to do.