• Basic forms
• 治る — to heal; get better / base form
• 治ります — gets better / masu form
• 治った — got better / ta form
• 治って — get better and … / te-form
• 治らない — doesn’t heal / negative
• 治れば — if it heals / conditional
• 治れ — heal! (rare) / imperative
• Common expressions
• 病気が治る — an illness heals
• けがが治った — an injury recovered
• More
• なかなか治らない — doesn’t heal easily

治る（なおる） is a godan verb. It describes something healing or being corrected naturally.

• Basic forms
• 治める — to govern; put in order / base form
• 治めます — governs; puts in order / masu form
• 治めた — governed; put in order / ta form
• 治めて — govern and … / te-form
• 治めない — don’t govern / negative
• 治めれば — if (you) govern / conditional
• 治めろ・治めよ — govern! / imperative
• Common expressions
• 国を治める — govern a country
• 問題を治める — bring a problem under control
• More
• 治められる — can govern; can put in order / potential

治める（おさめる） is an ichidan verb. You actively govern/control/put something in order — the transitive counterpart idea to 治る.