Question

Ches nao jup vs

Cho goc xAy tren tai Ax lay diem B va C (B nam giua A va C).Tren tai ay lay 2 diem D eva E sao cho AD=AB,AE=AC

CM

a,BE=DC

b,CM TAM GIAC OBC =ODE

Answer 1

a) Xét hai tam giác ABE và ADC có:

AB = AD (gt)

\(\widehat{A}\): góc chung

AC = AE (gt)

Vậy: \(\Delta ABE=\Delta ADC\left(c-g-c\right)\)

Suy ra: BE = CD (hai cạnh tương ứng)

b) Ta có: BC = AC - AB

DE = AE - AD

Mà AB = AD (gt)

AC = AE (gt)

\(\Rightarrow\) BC = DE

Ta lại có: \(\widehat{B_1}+\widehat{B_2}=180^o\)

\(\widehat{D_1}+\widehat{D_2}=180^o\)

Mà \(\widehat{B_1}=\widehat{D_1}\) (\(\Delta ABE=\Delta ADC\))

\(\Rightarrow\) \(\widehat{B_2}=\widehat{D_2}\)

Xét hai tam giác OBC và ODE có:

\(\widehat{B_2}=\widehat{D_2}\) (cmt)

BC = DE (cmt)

\(\widehat{C_1}=\widehat{E_1}\) (\(\Delta ABE=\Delta ADC\))

Vậy: \(\Delta OBC=\Delta ODE\left(g-c-g\right)\).