Question

Cho \(\Delta ABC\) có góc A=90⁰ .Gọi E là 1 điểm nằm trong tam giác đó 

CMR góc BEC là góc tù

Answer 1

H

Trong \(\Delta ABC\)có: \(\widehat{A}+\widehat{ABC}+\widehat{ACB}=180\Rightarrow90+\widehat{ABC}+\widehat{ACB}=180\Rightarrow\widehat{ABC}+\widehat{ACB}=90\)

Mà: \(\widehat{EBC}< \widehat{ABC};\widehat{ECB}< \widehat{ACB}\Rightarrow\widehat{EBC}+\widehat{EBC}< \widehat{ABC}+\widehat{ACB}=90\)(1) 

Mặt khác: Trong \(\Delta EBC\)có: \(\widehat{BEC}+\widehat{EBC}+\widehat{ECB}=180\)(2)

Từ (1) và (2), ta có: \(\widehat{BEC}>90\)

<=> BEC là góc tù.