Question

a) chứng minh: A'B'C' đồng dạng D'E'F'
b) chứng minh: B'C'.D'F'=A'C'.E'F'

Answer 1

Xét \(\Delta D'E'F':\)

\(\widehat{D'}+\widehat{E'}+\widehat{F'}=180^o\) (Tổng 3 góc trong tam giác).

\(\Rightarrow\widehat{D'}+60^o+50^o=180^o.\\ \Rightarrow\widehat{D'}=70^o.\\ \Rightarrow\widehat{D'}=\widehat{A'}\left(=70^o\right).\)

Xét \(\Delta A'B'C'\) và \(\Delta D'E'F':\)

\(\widehat{A'}=\widehat{D'}\left(cmt\right).\)

\(\widehat{B'}=\widehat{E'}\left(=60^o\right).\)

\(\Rightarrow\) \(\Delta A'B'C'\sim\) \(\Delta D'E'F'\left(g-g\right).\)

\(\Rightarrow\dfrac{B'C'}{E'F'}=\dfrac{A'C'}{D'F'}\) (2 cạnh tương ứng).

\(\Rightarrow B'C'.D'F'=A'C'.E'F'.\)