One way in which confucian teachings, the ten commandments, and the eight-fold path in buddhism were all similar?

The first step to answering your question is learning what these three systems of belief are, who initiated them, and for what purpose. Once we glimpse that purpose, we will know how all three have a commonality, even if they are essentially very different.

Let´s first start with the one that is not a system of religion, or a faith, but rather a civil system that directs how people are to behave in order to obtain the ultimate goal, which is peace and civilization. This is Confucianism. Confucianism was not intended, nor is it, a religion, like Buddhism or Judaism and Christianity. It was first proposed by Master Kong, who later became known as Confucius. What Confucius did was take the happenings of his time (551-479 BCE) in China, during the Zhou dynasty and propose a series of steps that if followed, would allow Chinese society to grow and become more coherent, more balanced and peaceful. Confucianism literally became a way of civil life, and did not interfere at all with the religious beliefs that China had at the time. These tenets of Confucianism, which were adopted by the Chinese, became a pathway to reach the highest goal, which was peace and civil unity.

Buddhism, unlike Confucianism is a religion and it was initiated by Siddhartha Guatama, who was believed to have reached the ultimate goal in life, entering Nirvana, or the heaven of Buddhists. To do so, he had to undertake a series of steps, which were later known as the Noble Eight-fold Path. This path, and its steps, would allow a human soul to start getting rid of its trappings to ascend liberated to Nirvana and stop the neverending cycle of Samsara, or rebirth. The likeness to Confucianism comes in that both of these systems propose and establish a set pathway through which either a person (in Buddhism), or a society (Confucianism) can reach liberation and peace.

Finally we have the Ten Commandments. Now, the Ten Commandments are neither a system, nor a religion. They are simply the roadmap that God provided to Moses on Mount Sinai as a means for His people, the Jews who had just been freed from Egypt, to live their lives so that they could both form their new nation (Israel), be preserved as a nation and also attain the ultimate goal, which was salvation. Like Confucianism and the Eight-fold Path of Buddhism, the Ten Commandments are the pathway through which first Jews, and then Christians, would be able to attain Heaven, and live peaceful lives on Earth that were acceptable to God.

So in the end, the answer to the question would be: All three of them provided the roadmap, or guideline, for believers to be able to finally achieve their end goals: a good life on earth, peace and in the case of Buddhism and Judaism and Christianity, achieve Heaven.

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