"同一"means one things E:你和John是同一个学校毕业的（graduate from a（同一） school） “一样”means that,two or three things are resemble ，similar ，alike。 E：yuor brother and you are twins,we can say“你和你哥哥长的一样” 1.“同样”means that extends from one thing to another thing . E:你能做的，同样，我也可以做。2.“同样”我和他做了同样（一样）的事情。Sometimes 同样and一样are similar ,they can exchange with each other.

1.同一：it has only patten ：“同一”+musure word+noun Sometimes the musure word can be dropped,but the meaning is not changed. ex①.我们在做同一件事情。(We are doing the same thing. ) ex②.我们买了同一本书。(We bought the same book.) ex③.他们是同一类人。(They are people of a kind) Notice：“件,本,类” in these sentence can not be dropped. But sometimes the musure word can be dropped,but the meaning is not changed. ex④.同一(种)款式，你只能买一件。(You can only buy one suit of one style) ex⑤.同一(类)问题，我只回答一次。（I’ll answer questions of one type only once ） notice：“种,类” in these sentence can be dropped. Generally “同一”is not followed by the structural particle“的”, especially the musure word is only one character.(but一样 and 同样can .) ex②.我们买了同一本书。(√)我们买了同一本的书。(×) 2.同样： ⑴ as an adj. patten1：“同样”+(的)+noun. ex①. 我和他有同样的爱好（He and I have the same hobby.） notice：If there is a numeber+measure word before the noun, the structural particle“的”can be dropped. ex②.同样(的)两个苹果,我选了那个。(I choose that one from the same two apples.) patten2：“同样”+ verb or adj. ex③.任何意见，我们都同样接受(We will accept any acvice in the same way) ex④.我和你同样高兴(I am happy as you.) ⑵ as a conj. the patten：“同样”+sentence ex⑤.星期一我上课，同样,星期三我也上课。(I have class on Mon.,also I have class on Wed. ) 3.一样：. ⑴ as an adj. patten1：“一样”+的+noun. It is same as “the patten1 of 同样 ⑴.,but whenever “的”can be dropped. ex①. 我和他有一样的爱好(√)（He and I have the same hobby.） 我和他有一样爱好(×) patten2：“一样”+ verb or adj. It is same as “the patten2 of 同样 ⑴., ex②.任何意见，我们都一样接受(We will accept any acvice in the same way) ex③.我和你一样高兴(I am happy as you.) ⑵. difference between 一样 and 同样： Ⅰ “同样”can not be use as a predicate，but “一样”can.. ex①.这两本书一样。(√) (These two books are same.) 这两本书同样。(×) Ⅱ “同样”can not be use as a complement, but “一样”can. ex③.她们穿得一样。(√) (They dressed alike.) 她们穿得同样。(×) Ⅲ.The negative adverb “不”can only be used before“一样”， but can not be used before“同样”. ex④.这两本书不一样(√) (these two books are not same.) 这两本书不同样(×) Notice： in Chinese there is only “不一样”, “不同样”is inexistent 4.According to “同一”is not followed by the structural particle“的”,( (but一样 and 同样can .),so the answer should be： 我和我哥哥有 同样（or 一样） 的爸爸妈妈。(My brother and I have the same parents.) 真巧了！我们今天在穿 同样（or 一样）的衬衫。

0.0

basically 同样and 一样are interchangeable when both of them are placed in front of a noun that functions as an adjective. however, if there is no noun following them, you can only use 一样 like: 我们吃的一样，我们穿的一样 but you can't say 我们穿的同样 it's weird for 同一， it refers to "the same one", the "one" can be one category, one place etc. so here is a context: 我们在同一所学校上学/ 我们上的学校一样/ 我们在同样的学校上学（this one may refer to either the same school or the same kind of school like public or private school）.

hey,simple to answer the question. "同一"，"同样"，"一样" all have “ the very same one” meaning ,but if you want to describe something is only one and unique,you have to use "同一".hope can help you :)