Bài 29 câu d
vi D doi xung voi A qua H suy ra H la trung diem cua AD
Ta co AB//DN(dt di qua D//AB cat AC tai N)
ABvuong goc voi AC(tam giac ABC vuong tai A)
Suy ra DN vuong goc AC tai N(tu vuong goc den //)
Xet tam giac ADNvuong tai N (DN vuong goc AC taiN)co
​:NH la duong trung tuyen ung voi AC (H la trung diem AD)suy ra NH=AH=DH=AD/2
suy ra tam giac ANH can tai H suy ra goc HAN= goc HNA
Co: goc BAH +goc ABH=90do ; goc BAH+goc HAN=goc CAB =90 do
Suy ra goc ABH=goc HAN (cung phu voi goc BAH)
ma goc ABH=goc NMC(2 goc dong vi;AB//DN)
goc HAN=goc HNA nen goc NMC=goc HNA (1)
Xet tam giac MNC vuong tai N co NI la trung tuyen ung voi canh huyen nen NI=IM=IC=NM/2
suy ra tam giac MIN can tai I suy ra goc IMN=goc INM hay goc NMC =goc INM (2)
tu (1);(2) suy ra goc HNA=goc INM
suy ra goc HNA +goc HND=goc INM+goc HND
goc AND=goc HNI
nen goc HNI=90 do(do goc AND=90 do)
Suy ra HN vuong goc voi NI tai N(dpcm)

bài 29 câu c