Question

Cho tam giacABC vuong o A(AB<AC), duong cao AH. Goi D la diem doi xung cua A qua H. Duong thang  ke qua D va song song voi AB no cat BC va AC lan luot o M va N.

a.Tu giac ABDM la hinh j?

b. Chung minhM la truc tam tam giac ACD

c. Goi I la trung diem cua MC. Chung minh goc HNI  vuong

Answer 1

a,vi bh la dung cao ad h la trung diem ad suy ra tam giac bda can tai b suy ra b=180-bad/2 (1)

vimh vuong goc ad h la trung diem ad suy ra tam giac dma can tai m suy ra m=180-adm/2 ( 2)

vi ab//dn suy ra bad=adm (3)

tu 1 2 3 suy ra abd=dma (4)

vi tam giac abd can tai b suy ra bad=bda (5)

tam giac abm can tai m suy ra adm=dam (6)

tu 3 5 6 suy ra bda=dam suy ra bam=bdm (7)

tu 4 va 7 suy ra tu giac bdma la hinh binh hanh co bm vung goc ad suy ra tu giac abdm la hinh thoi

b,vi dn vung goc ac ch vuong goc voi ad ch va dn cat nhau tai m suy ra m la truc tam cua tam giac acd

c,