i happened ____(see) my teacher on the way to sch

是to see，在上学的路上，我碰巧遇到老师。

happen是不及物动词，它的用法常见的有如下几种情况：

1. 表示“某地(某时)发生了什么事”，常用“sth.+ happen +地点/时间”这一结构来表达，此时主语应是事情。例如：

The story happened in 2003. 这个故事发生在2003年。

An accident happened in that street. 那条街上发生了一起事故。

2. 表示“某人出了某事(常指不好的事)”，要用“sth.+ happen+to sb.”这一结构来表达。例如：

A car accident happened to her this morning. 今天上午她发生了交通事故。

What happened to you? 你怎么啦？

3. 表示“某人碰巧做某事”，要用“sb.+ happen+ to do sth.”这一结构来表达。例如：

I happened to meet a friend of mine in the street yesterday. 昨天我碰巧在街上遇到了我的一个朋友。

4. happen表示“碰巧或恰巧发生某事”时，还可用“It happens / happened that...”这一结构来表达。例如：

It happened that Brian and Peter were at home that day. 碰巧那天布莱恩和彼得在家了。

It happened that he had to take part in a meeting that afternoon. 碰巧那天下午他不得不参加一个会议。

注：that从句中的主语是人时，此种结构可以与“sb.+ happen + to do sth.”结构互换。例如：

It happened that Brian and Peter were at home that day. = Brian and Peter happened to be at home that day.