问题 填空题

在等边三角形ABC中,点E在直线AB上,点D在直线BC上,且ED=EC,若三角形ABC的边长为1,AE=2,则CD的长为______.

答案

当E在线段BA的延长线上,D在线段BC的延长线上时,如图1所示,

过E作EF⊥BD,垂足为F点,可得∠EFB=90°,

∵EC=ED,∴F为CD的中点,即CF=DF=

1
2
CD,

∵△ABC为等边三角形,∴∠ABC=60°,

∴∠BEF=30°,

∵BE=AB+AE=1+2=3,

∴FB=

1
2
EB=
3
2

∴CF=FB-BC=

1
2

则CD=2CF=1;

当E在线段AB的延长线上,D在线段CB的延长线上时,如图2所示,

过E作EF⊥BD,垂足为F点,可得∠EFC=90°,

∵EC=ED,∴F为CD的中点,即CF=DF=

1
2
CD,

∵△ABC为等边三角形,∴∠ABC=∠EBF=60°,

∴∠BEF=30°,

∵BE=AE-AB=2-1=1,

∴FB=

1
2
BE=
1
2

∴CF=BC+FB=

3
2

则CD=2CF=3,

综上,CD的值为1或3.

故答案为:1或3

阅读理解

There are many theories about the beginning of drama in ancient Greece. The one most widely accepted today is based on the assumption that drama evolved (演化) from ceremony. The argument for this view goes as follows.

In the beginning, human beings viewed the natural forces of the world --- even the seasonal changes --- as unpredictable, and they sought through various means to control these unknown and feared powers. Those measures which appeared to bring the desired results were then kept and repeated until they hardened into fixed ceremonies. Eventually stories arose which explained the mysteries of the ceremonies. As time passed some ceremonies were abandoned, but the stories, later called myths, remained and provided material for art and drama.

Those who believe that drama evolved out of ceremony also argue that those ceremonies contained the seed of theater because music, dance, masks, and costumes were almost always used. Furthermore, a suitable site had to be provided for performances and when the entire community did not participate, a clear division was usually made between the "acting area" and the "auditorium ". In addition, there were performers, and, since considerable importance was attached to avoiding mistakes in the performing of ceremonies, religious leaders usually took that task. Wearing masks and costumes, they often acted other people, animals, or supernatural beings, and imitated the desired effect --- success in hunt or battle, the coming rain, etc. as an actor might. Eventually such dramatic representations were separated from religious activities.

Another theory traces(追溯) the theater's origin from the human interest in storytelling. According to this view, tales (about the hunt, war, etc) are gradually developed, at first through the use of action and dialogue, and then through the assumption of each of the roles by a different person. A closely related theory traces theater to those dances that are primarily rhythmical and gymnastic or that are imitations of animal movements and sounds.

小题1:Which is the best title of the passage?

A.Religious activities in ancient Greece.

B.The ceremonies in ancient Greece.

C.Drama theories.

D.The origin of Greek Drama.小题2:According to the passage, drama_______________.

A.was played in memory of ancient Greek ceremonies

B.was a form of ceremony played by ancient Greeks to control unknown powers

C.evolved out of ancient Greek ceremonies with time passing by

D.is one of the measures Ancient Greeks took to view natural forces小题3:In tracing the beginning of drama, which of the following is not mentioned?

A.Planting.

B.Religious ceremonies.

C.Gymnastic.

D.Storytelling.

填空题