Question

[Tran Bao Chau]

cho\(\Delta\)ABC.ve duong thang song song voi BC ,cat AB tai D va cat AC tai E . qua C ke tia Cx \(//\)AB, cat DE tai G.

a, tu giac BDGC la hinh gi ?vi sao

b,cm DA*EG=BD*DE

c,cm \(\Delta\)ABC dong dang \(\Delta\)CGE

giai nhanh gium minh nha !!!!

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Answer 1

[Lê Anh Tú]

A B C E G n D

ý a dễ rồi bn tự làm.

b) Do GC//AD\(\Rightarrow\frac{GC}{AD}=\frac{GE}{DE}=\frac{CE}{AE}\left(1\right)\)

Do EG//BC \(\Rightarrow\frac{AD}{DB}=\frac{AE}{CE}=\frac{DE}{BC}\left(2\right)\)

Từ (1) và (2) => \(\frac{DA}{DB}=\frac{DE}{GE}=DA.GE=DB.DE\)

c) \(\widehat{GEC}=\widehat{AED}\left(đđ\right)\)

\(\widehat{AED}=\widehat{ACB}\)

\(\Rightarrow\widehat{GEC}=\widehat{ACB}\)

Xét \(\Delta GEC\)và \(\Delta ACB\)

\(\widehat{CCA}=\widehat{CAB}\)

\(\widehat{GEC}=\widehat{ACB}\)

=> đpcm (khúc c mk cũng chưa chắc)