Question

Cho hình vẽ:

Chứng minh rằng: góc A1 + góc C2 = góc B + góc D

Answer 1

Xét tứ giác ABCD có :

\(\widehat{A}+\widehat{B}+\widehat{C}+\widehat{D}=360^0\)

\(\Rightarrow\widehat{B}+\widehat{C}=360-\widehat{A}-\widehat{C}\)(1)

Ta có : \(\widehat{A_1}=180-\widehat{A}\)(2 góc kề bù )

\(\widehat{C_1}=180-\widehat{C}\)(2 góc kề bù )

\(\Rightarrow\widehat{A_1}+\widehat{C_1}=180-\widehat{A}+180-\widehat{C}=360-\widehat{A}-\widehat{C}\)(2)

Từ 1 và 2 suy ra :

\(\widehat{B}+\widehat{C}=\widehat{A_1}+\widehat{C_1}\)(đpcm)