You have a few options.
One would to load all the sub pages on the initial page load but have only the active one showing. When one of the menu items is clicked the content is switched out via javascript (ie, hide the current page, show the new page).
Another option would be to have javascript make an AJAX call to grab the data for the selected menu item and then switch out the current article for the selected one.
The first option would increase page load time slightly but loading each article afterwards would be instant. The second option wouldn't increase the initial load time but when the menu items are clicked there will be a slight delay as the browser waits for the selected article's data to return from the server.
Another completely different option would be to have an iframe and load the articles in the iframe (you can use the tmpl=component query variable to only load the article in the iframe, without the rest of the template). I don't recommend this route for a number of reasons (SEO, usability, mobile-friendliness, etc).