Why was finding a close relationship between mitochondrial DNA and bacterial DNA considered particularly strong evidence in favor of the endosymbiosis theory

Endosymbiosis theory: It confirmed a fundamental prediction made by the hypothesis and have great evidences and could not be explained by any alternative hypothesis.

Explanation:

Both bacteria and mitochondrial DNA are in circular form.  

Both bacteria and mitochondria contain 70S chromosome, both have their own replicating machinery.

According to endosymbiosis theory :

The host cell provided a protected environment and carbon compounds for the endosymbiont;  and in return ,the endosymbiont provided increased ATP from the carbon compounds.

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Allow large amino acids through