How to use linux tools to verify a site's authenticity

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http://unix.stackexchange.com – When I go to certain websites where it's important for me to know that I'm connected securely, certain browsers will say that the site failed the authenticity check. Firefox won't say anything, but even though Firefox is my favorite browser, I don't completely trust it lol. I've been having a problem with security and hackers, so it's important that I can determine with a high degree of certainty whether or not the site is authentic, and why some browsers are saying it's not but Firefox says it is. It appears that the site I'm connecting to has four certificates, and one of them was not sign (HowTos)