Question

[tran duc huy]

Cho tg ABC can tai A (A<90⁰) . Ke BH vuong goc vs AC, CKvuong goc vs AB. Goi M la giao diem cua BH va CK

a,CM tg HAB=tg KAC

b,CM:KH//BC

c,Goi N la trung diem cua BC. Chứng minh A,M,Nthang hàng

Answer 1

[Ju Moon Adn]

Answer 2

[Ju Moon Adn]

a, Xet tg vuong HAB va tg vuong KAC co:

AB=AC(hai canh ben tg can ABC)

BAC chung

Do do tg vuong HAB=tg vuong HAC(ch-gn)

b,Vi tg HAB=tg KAC (cau a)

=>HA=KA(2 canh t/u)

Xet tg AKH co :

HA=KA(cmt)

=>tg HAK can tai A(d/n tg can)

=>AKH= \(\dfrac{180^0-BAC}{2}\) (1)

Vi tg ABC can tai A :

=> ABC= \(\dfrac{180^0-BAC}{2}\) (2)

Tu (1) va (2)

=> AKH =ABC mà 2 góc này ở vị trí hai góc đồng vị

=>KH//BC(dpcm)

c, Xet tg vuong AKM va tg vuong AMH co:

AM chung

KA=AH(cau a)

do do :tg vuong KAM=tg vuong HAM(ch-gn)

=>KAM=HAM(2 goc t/u)

Ma tia AMnam giua hai tia KAva AH

=>AM la tia phan giac KAH (3)

Xet tg BAMva tg ACN co:

AB=AC(2 canh ben tg ABC can)

ABC=ACB(2 goc o day tg can ABC)

BN=CN(N la td BC)

Do do tg ABN=tg ACN(c.g.c)

=>BAN=NAC(2 goc t/u)

Ma tia AN nam giua hai tia AB va AC

=> AN la tia p/g BAC (4)

Tu (3) va (4)

=>3 diem A,M,N thang hang