Cho tam giac ABC co duong trung tuyen AM Qua diem D Thuoc BC va duong thang song song voi AM cat AB va AC theo thu tu tai E va Fa, khi D di chuyen tren BC thi tong DE_DF ko doi b, Qua diem A ke duong thag song song BC cat EF tai K CMR K la trung diem cua EF
Cho tam giac ABC can tai A co AD la duong trung tuyen
a)Chung minh tam giac ABD= tam gaic ACD va AD vuong goc voi BC
b)Cho AB=10cm,BC=16cm. Tinh do dai AD va so sanh cac goc cua tam giac ABC.
c) Ve duong trung tuyen CF cua tam giac ABC cat AD tai M. Tinh do dai AM.
d) Ve DH vuong goc AC tai H, tren canh AC va canh DC lan luot lay hai diem E,K sao cho AE=AD va DK=DH. Chung minh: EK vuong goc voi BC
A,
xét \(\Delta ABD\)và \(\Delta ACD\)
CÓ \(\hept{\begin{cases}AB=AC\\chungAD\\BD=DC\end{cases}}\)
SUY RA \(\Delta ABD\)=\(\Delta ACD\) (C.C.C) (1)
=> \(\widehat{BDA}\)=\(\widehat{CDA}\)
MÀ \(\widehat{BDA}\)+\(\widehat{CDA}\)=180
=> \(\widehat{BDA}\)=\(\widehat{CDA}\)=90
B, (1) => BC=DC=1/2 BC=8
ÁP DỤNG ĐỊNH LÍ PITAGO TA CÓ
\(AB^2=AD^2+BD^2\)
=> AD^2=36
=>AD=6
bai 1co tam giac abc can tai a tren tia doi cua cac tia bc va cb lay hai diem d va e sao cho ce = bd goi m la trung diem cua bc tu b va c ke bh vuong goc voi ad va ck vuong goc voi ae .cm 3 dt bh ck va am cung di qua mot diem
bai 2 cho tam giac abc vuong tai a goc c bang 30 do duong cao ah tren doan hc lay diem d sao cho hd=hb tu c ke ce vuong goc voi ad cmr
a, tam giac abd deu
b,eh song song voi ac
bai 3 cho tam giac abc co goc a = 90 do qua a ke dt d tu b va c ke bd vuong goc voi dt d va ce vuong goc voi dt d tinh do dai de theo bd va ce
bai 4 cho tam giac abc vuong tai a hai duong phan giac bm va cn tu m va n ke mmphay va nnphay vuong goc voi bc cmr goc mphayanphay bang 45 do
cho tam giac abc tren tia doi cua tia ab lay diem d sao cho ad=ab tren tia doi cua tia ac lay diem e sao cho ae=ac mot duong thang di qua a cat cac canh de va bc theo thu tu o m va n.chung minh rang:
a)bc//de
b)am=an
Cho tam giac ABC vuong can tai A. Tren AB lay diem D, tren AC lay diem E sao cho AD=AE. Cac duong thang vuong goc ke tu A va E voi CD cat BC o G va H. Duong thang EH va BA cat nhau o M.
a)CM: Tam giac ACD=tam giac AME
b)BG=GH
bai 1 cho hinh thang can abcd va ab<cd ke ac duong cao ah va bk ua hinh thang goi m la trung diem ad va n la trung diem bc m va n lan luot cat bd tai e va ac tai d biet ab =4cm cd = 10 cm tinh ef
bai2 cho tam giac abc can tai a co ab>bc 2 dg trung tuyen ad va be duong thang qua e // bc cat ab tai f goi i va k lan luot la trung diem bf va ce biey ik = 7,5 ad= 12 tinh bcc va tinh chi vi hinh thang
bai 3cho tu giac abcd co goc a = goc d , goc b + goc c = 180 goi m , n theo thu tu la trung diem bc va ad a) cm abd la hinh vuong b) cm am = dm c) cho ab = 3cm ad= 4m bc= 5cm tinh mn
GIUP MINK VS
THANKS NHIEUUUUUUUUUU LAM
Cho tam giac ABC co trung tuyen AM tu diem P tren AM ve 2 duong thang song song voi AB va AC cat BC theo thu tu tai I va J. Chung minh m la trung diem cua IJ
Cho (O) duong kinh AB. Tren duong tron lay diem C sao cho AC<BC (C khac A). Cac tiep tuyen tai B va C cua (O) cat nhau o D, AD cat (O) tai E (E khac A)
1. CM: BE2= AE.DE
2. Qua C ke dt song song voi BD cat AB tai H, DO cat BC tai F. Chung minh tu giac CHOF noi tiep
3. Goi I la giao diem cua AD va CH. Chung minh I la trung diem cua CH
cho tam giác ABC co góc A=90 do va ab=ac tren canh ab va ac lay d va e sao cho ae=ad tu a va d ke dg thang vuong goc vs be cat bc tai m va n tia md cat tia ca o I cm a la trung diem cua ci va cm=mn
