先针对你的两个例句，这两句应该是定语从句，who/that teaches 作为定语修饰 a person：
定语从句中who，that在很多情况下可以通用，但是有些情况只能用who:
1. 先行词是one, ones, anyone的时候宜用who.
One who has nothing to fear for oneself dares to tell the truth.
The ones who flatter me don’t please me.
Don’t tell anyone about the news who oughtn’t to know it.
Anyone who fails to finish the task given should be criticized.
2. 先行词为those的时候，宜用who为关系代词
Those who were not fit for their work could not see the beautiful clothes
made of the magic cloth.
Those who want to go to the Great Wall sign up here.
3. 当先行词有比较长的后置定语的时候
I met a foreigner in the street yesterday who could asked me questions in
Chinese.
4. 一个句子中带有两个定语从句，其中一个定语从句的关系代词为that,另一个则用
who.
The boy that you met last night is the group leader who studies very hard.
5. 在there be 开头的句子中
There is an old man who wants to see you.
There are many young men who are against him.
然后是针对题目主干中的问题“在宾语从句中如何正确使用that, who, which, whom,(还有哪些关系代词)”
一、宾语从句的定义：
用作宾语的从句叫宾语从句。宾语从句可以用连词that，连接代词who，whom，what，which；连接副词 how，when，where以及if和whether引起。连接代词和连接副词在宾语从句中作一相应的句子成分，if或whether表示疑问，而that没有意义仅起连接作用。
二、宾语从句的分类：
1． 作动词的宾语从句：
如：Everyone knows that he is a good student.
He wondered how the pyramids were built.
2． 作介词宾语：
如：This depends on how hard you work.
Is there anything wrong in what I said?
3． 作形容词的宾语：
如：They are confident that they can do the job well.
I am not certain whether the train will arrive on time.
三：使用宾语从句要注意的问题：
1． 宾语从句引导词that的省略：
在非正式场合下，that在引导宾语从句时，可以省略。
如：I think (that) you are right.
2． 形式宾语it：
如果宾语从句后面跟有补语，要用形式宾语it来代替，而将从句放到补语的后面去。如：He has made it clear that the meeting will not be postponed.
I heard it said that that factory was founded in 1901.
3．宾语从句的时态呼应：
如果主句的谓语是过去时，宾语从句的时态要按照时态呼应规则进行相应的调整。但是若宾语从句表示的是客观真理或自然观念，其谓语时态仍用一般现在时。
如：He said that he had left his umbrella in the library.
The teacher told the students that the Pacific Ocean is the largest ocean in the world.
4． 宾语从句否定意义的转移：
在think, believe, suppose, expect 等动词所根的宾语中，如果从句谓语是否定的，一般要将否定词not转移至主句谓语上去，而将从句宾语变为肯定形式。
如：I don’t think he has time to play chess with you.
I don’t suppose it is the rush hour yet.
5．一些动词接的宾语从句通常要用虚拟语气：
一般说来，在一些表示坚持(insist)，命令(order，command)，建议(suggest，advise)，要求(require，demand) 等动词之后的宾语从句中，谓语一般要用“should +动词原形”（其中的should在美国英语中常省略，但是引导从句的that通常不省略）：
如：She suggested that we (should) leave early．
He ordered that the medicine (should) be sent by a special plane．
6．whether 与 if
引导介词宾语从句时，只能用 whether，不用if；与“or not”连用时，一般用whether，不用if。
如：I am interested in whether he'll go abroad．
We don't know whether he will come or not．
7．宾语从句的语序
连接词后面为陈述语序。
如：I don’t know what your name is.
8．直接引语变为间接引语
间接引语的使用应注意选择合适的动词。陈述用say／tell，疑问用ask／wonder，而祈使用 tell／order，建议用advise／suggest。注意这些动词后面的结构和语气。
如：“Could you get some tea for me？” Mr．Blake said to his wife．
→Mr. Blake asked his wife whether she could get some tea for him.
“Shall we go dancing tonight？”John said．
→John suggested they should go dancing tonight.
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