Question

[Tiểu muội]

Giúp mình vs,Thanks

Answer 1

[Thanh Hoàng Thanh]

a) Xét \(\Delta ADE\) và \(\Delta ABC:\)

\(AD=AB\left(gt\right).\\ AE=AC\left(gt\right).\)

\(\widehat{DAE}=\widehat{BAC}\) (2 góc đối đỉnh).

\(\Rightarrow\Delta ADE=\Delta ABC\left(c-g-c\right).\)

b) Ta có: \(\widehat{OBE}=180^o-\widehat{ABC};\widehat{ODC}=180^o-\widehat{ADE}.\)

Mà \(\widehat{ABC}=\widehat{ADE}\left(\Delta ABC=\Delta ADE\right).\)

\(\Rightarrow\widehat{OBE}=\widehat{ODC}.\)

Ta có: \(BE=BA+AE;DC=DA+AC.\)

Mà \(BA=DA;AE=AC\left(gt\right).\)

\(\Rightarrow BE=DC.\)

Xét \(\Delta OBE\) và \(\Delta ODC:\)

\(\widehat{OBE}=\widehat{ODC}\left(cmt\right).\\ BE=DC\left(cmt\right).\\ \widehat{BEO}=\widehat{DCO}\left(\Delta ADE=\Delta ABC\right).\\ \Rightarrow\Delta OBE=\Delta ODC\left(g-c-g\right).\)

c) \(\Delta OBE=\Delta ODC\left(cmt\right).\)

\(\Rightarrow OB=OD\) (2 cạnh tương ứng).

d) Xét \(\Delta OAE\) và \(\Delta OAC:\)

\(OAchung.\\ OE=OC\left(\Delta OBE=\Delta ODC\right).\\ AE=AC\left(gt\right).\\ \Rightarrow\Delta OAE=\Delta OAC\left(c-c-c\right).\)

\(\Rightarrow\widehat{AOE}=\widehat{AOC}\) (2 góc tương ứng).

\(\Rightarrow OA\) là tia phân giác của \(\widehat{COE}.\)