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)
a)xét ΔABD và ΔFED có:
\(\widehat{BAD}=\widehat{BFD}=90^o\)
BD là cạnh chung
\(\widehat{ABD}=\widehat{FBD}\)(BD là phân giác của \(\widehat{ABF}\))
⇒ΔABD=ΔFED(c.huyền.g.nhọn)
b)gọi I là giao điểm của AF và BD
xét ΔABI và ΔFBI có:
BF=AB(ΔABD=ΔFED)
BI là cạnh chung
\(\widehat{ABI}=\widehat{FBI}\)(BD là phân giác của \(\widehat{ABF}\))
⇒ΔABI=ΔFBI(c-g-c)
⇒\(\widehat{BIA}=\widehat{BIF}\)(2 góc tương ứng)(1)
Mà \(\widehat{BIA}+\widehat{BIF}=180^o\)(2 góc kề bù)(2)
từ (1) và (2) ⇒\(\widehat{BIA}=\widehat{BIF}=\dfrac{180^o}{2}=90^o\)
vì ΔABI=ΔFBI⇒IA=IF
Do đó:BD là trung trực của AF(đ.p.cm)
c)xét ΔDCF có
DC là cạnh huyền
⇒DC>DF
Mà DF=AD
⇒DC>AD
d)Ta có:
AB=DF(ΔABD=ΔFED)
Mà AE=FC
⇒AB+AE=DF+FC
hay BE=DC
xét ΔBDC và ΔBDE có:
BE=DC(ch/m trên)
\(\widehat{EBD}=\widehat{CBD}\)(BD là phân giác của \(\widehat{EBC}\))
BD là cạnh chung
⇒ ΔBDC=ΔBDE(c-g-c)
⇒\(\widehat{BDE}=\widehat{BDC}\)(2 góc tương ứng)
Mà \(\widehat{BDA}=\widehat{BDF}\)(ΔABD=ΔFED)
⇒\(\widehat{BDE}-\widehat{BDA}=\widehat{BDC}-\widehat{BDF}\)
hay \(\widehat{ADE}=\widehat{FDC}\)(đ.p.cm)
ta có:\(\widehat{ADE}+\widehat{CDE}=180^o\)(2 góc kề bù)
Mà \(\widehat{ADE}=\widehat{FDC}\) ⇒\(\widehat{FDC}+\widehat{CDE}=180^o\)
hay E,D,F thẳng hàng(đ.p.cm)