题目

Dog owners now have a little help understanding their furry friends . A new device called Bow-Lingual “translates” dog barks into English , Korea or Japanese. Bow-Lingual’s Japanese inventors spent much time and money analyzing dog barks . They found that dog noises can be broken down into six different emotions : happiness , sadness , frustration , anger , assertion and desire . Part of the Bow-Lingual device hangs on the dog’s collar . The other part is a handle-held unit for the owner . When the dogs barks , the unit displays translated phrases . Some people have scoffed at Bow-Lin在矩形ABCD中，点E在BC边上，过E作EF⊥AC于F，G为线段AE的中点，连接BF、FG、GB．设=k．（1）证明：△BGF是等腰三角形；（2）当k为何值时，△BGF是等边三角形？（3）我们知道：在一个三角形中，等边所对的角相等；反过来，等角所对的边也相等．事实上，在一个三角形中，较大的边所对的角也较大；反之也成立．利用上述结论，探究：当△BGF分别为锐角、直角、钝角三角形时，k的取值范围．