Question

cho hình thang cân ABCD (AB//CD) , AB<CD . Kẻ các đường cao AH , BK . Chứng minh rằng :

a) AH=BK

b) DH=CK

Answer 1

a)Xét hình thang cân \(ABCD\)\((AB//CD)\):

\(\Rightarrow\left\{{}\begin{matrix}\widehat{D}=\widehat{C}\\AD=BC\end{matrix}\right.\text{(t/c)}\)

Xét \(\Delta ADH;\Delta BCK\):

\(\left\{{}\begin{matrix}\widehat{AHD}=\widehat{BKC}\left(=90^o\right)\\AD=BC\text{(cmt)}\\\widehat{D}=\widehat{C}\text{(cmt)}\end{matrix}\right.\)

\(\Rightarrow\Delta ADH=\Delta BCK\left(ch-gn\right)\)

\(\Rightarrow AH=BK\text{(2 cạnh tương ứng)}\)

b)Vì \(\Delta ADH=\Delta BCK\text{(cmt)}\)

\(\Rightarrow DK=CK\text{(2 cạnh tương ứng)}\)