Question

Cho hình thang ABCD(AB//CD), AB<CD. CMR: \(\widehat{A}+\widehat{B}>\widehat{C}+\widehat{D}\)

Answer 1

Kẻ BE // AD ; E ∈ CD ⇒ ABED là hình bình hành

⇒ \(\widehat{D}=\widehat{ABE}\)  \(;\)  \(\widehat{A}=\widehat{BED}\)

Ta có: \(\widehat{A}=\widehat{BED}>\widehat{C}\) \(;\) \(\widehat{ABC}=\widehat{ABE}=\widehat{D}\)

Suy ra: \(\widehat{A}+\widehat{B}>\widehat{C}+\widehat{D}\) ( đpcm )

Answer 2

Kẻ H // AD,H\(\in\)CD \(\Rightarrow\) ABHD là hình bình hành

\(\Rightarrow\)\(\widehat{ABH}=\widehat{D}\) ; \(\widehat{BHD}=\widehat{A}\)

Ta có:

\(\widehat{BHD}=\widehat{A}>\widehat{C}\) ; \(\widehat{ABC}>\widehat{ABH}=\widehat{D}\)

\(\Rightarrow\)\(\widehat{A}+\widehat{B}>\widehat{C}+\widehat{D}\)