Question

[PHAM PHUONG LINH]

Cho tam giac ABC co B^=C^.Tia phan giac cua goc A cat BC tai D. Chung minh rang:

a)Tam giac ADB=tam giac ADC

b)AB=AC

Answer 1

[Hoàng Thanh Huyền]

a) Ta có: \(\widehat{ADB}=180^o-\widehat{BAD}-\widehat{B}\)

\(\widehat{ADC}=180^o-\widehat{CAD}-\widehat{C}\)

Mà \(\widehat{BAD}=\widehat{CAD};\widehat{B}=\widehat{C}\)

Suy ra: \(\widehat{ADB}=\widehat{ADC}\)

Xét \(\Delta ADB\)và \(\Delta ADC\)có:

\(\widehat{ADB}=\widehat{ADC}\left(cmt\right)\)

\(ADchung\)

\(\widehat{BAD}=\widehat{CAD}\)

\(\Rightarrow\Delta ADB=\Delta ADC\left(gcg\right)\)

b) Từ \(\Delta ADB=\Delta ADC\)ta có: 

\(AB=AC\)(2 cạnh tương ứng)

Answer 2

[Yêu nè]

 

Xét \(\Delta ABC\) có \(\widehat{B}=\widehat{C}\)

\(\Rightarrow\Delta ABC\)cân tại A

\(\Rightarrow AB=AC\)

Xét \(\Delta ADB\) và \(\Delta ADC\) có

AD : chung

\(\widehat{DAB}=\widehat{DAC}\)(GT)

AB=AC  (cmt)
\(\Rightarrow\Delta ADB=\Delta ADC\) (c-g-c)

                                                         Học tốt