题干

我们在学习三角形相似时,往往是添加平行线构造相似三角形的基本图形.有一学生根据这一理论猜想三角形内角平分线有这样一个性质:如图,在△ABC中,AD平分∠BAC,则
B
D
C
D
=
A
B
A
C
.如果你认为这个猜想是正确的,请写出一个完整的推理过程.
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答案(点此获取答案解析)

证明:过点D作DE∥AB交CA于点E,

∵DE∥AB,

∴∠EDA=∠BAD,

∵AD平分∠BAC,

∴∠BAD=∠EAD,

∴∠EDA=∠EAD,

∴EA=ED,

∵DE∥AB,

CDBD

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                        The Power of -atlon(决心)

    The little country schoolhouse was heated by an old mal stove(火炉).A little boy had the job of coming to school early each day to start the1and warm the room before his teacher and his classmates got there

    One morning they 2to find the schoolhouse burning. They dragged(拖)the little boy out of the building more dead than alive. Then he was 3taken to a nearby county hospital.

    The doctor told the boy's mother that4 the lower part of his body was seriously burnt, he couldn't use his legs anymore. However, the5boy made up his mind that he would walk. Unluckily his thin legs6hung there, all but lifeless.

    Finally he returned home from the7.Every day his mother would press his little legs, but there was no feeling, no control,8.Yet his determination that he would walk was as 9as ever.

    When he wasn't in bed, he would sit in a wheelchair. One sunny day his mother wheeled him out into the yard to get some fresh air. This day, instead of sitting there, he 10himself from the chair and pulled himself across the grass,dragging his11behind him.

    He worked his way to the white fence(栅栏)around the yard. With great effort, he raised himself up on the fence. Then, he began dragging himself along the fence,12that he would walk. He started to do this every day. There was nothing he 13more than to develop life in those legs.

    In the end,through his determination he did14.He began to walk to school,then to run to school,to run15the joy of running. Later in college he made the running team.

      Still later in Madison Square Garden this determined young man, Dr. Glenn Cunningham, ran the world's fastest mile!