Question

cho tam giác ABC vuông tại C có góc A =60⁰,phân gics của góc BAC cắt BC ở E ,kẻ EK vuông góc AB,kẻ BD vuông góc với tia AE(D thuộc tia AE).CM:

a, AC=AK & AE vuông góc CK

b, KA=KB

c, EB>AC

đ, 3 đường thẳng AC,BD,KE cùng đi qua 1 điểm

Answer 1

a) cm tam giac ACE= tam giac AEK ( ch-gn)--> AC=AK

ta co : AC= AK 

          CE=EK ( tam giac ACE= tam giac AEK)

--> A,E nam tren duong trung truc cua CK

--> AE la duong trung truc CK->AE vuong goc CK

b)xet tam giac ABC vuong tai C ta co : goc A+ goc B =90 ( 2 goc phu nhau )

-->60+goc B=90--> goc B =30

ma goc EAB=1/2 A ( AE la tia p/g goc A)--> goc EAB=1/2.60=30

vay goc EAB = goc B

tuong tu : cm goc AEK = 90- EAK =90-30=60

          goc EBK=90- goc KEB =60

--> goc AEK= goc EBK

--> cm tam giac AEK = tam giac EBK ( g=c=g)

--> KA=KB

c) tu diem A den duoing thang CB ta co

AE la duong xien , AC la duong vuong goc===> AC< AE ( quan he duong xien duong vuong goc)

mã EB=EA ( tam giac AEK= tam giac EKB)

nen AC<BE

            d_ xet tam giac AEB ta co

EK la duong cao, ( EK vuong foc AB)

BD la duong cao ( BD vuong foc AE

AC la duong cao ( AC vuong goc BC )

==> EK,BD,AC dong quy tai 1 diem

Answer 2

a) cm tam giac ACE= tam giac AEK ( ch-gn)--> AC=AK
ta co : AC= AK 
          CE=EK ( tam giac ACE= tam giac AEK)
--> A,E nam tren duong trung truc cua CK
--> AE la duong trung truc CK->AE vuong goc CK
b)xet tam giac ABC vuong tai C ta co : goc A+ goc B =90 ( 2 goc phu nhau )
-->60+goc B=90--> goc B =30
ma goc EAB=1/2 A ( AE la tia p/g goc A)--> goc EAB=1/2.60=30
vay goc EAB = goc B
tuong tu : cm goc AEK = 90- EAK =90-30=60
          goc EBK=90- goc KEB =60
--> goc AEK= goc EBK
--> cm tam giac AEK = tam giac EBK ( g=c=g)
--> KA=KB


c) tu diem A den duoing thang CB ta co
AE la duong xien , AC la duong vuong goc===> AC< AE ( quan he duong xien duong vuong goc)
mã EB=EA ( tam giac AEK= tam giac EKB)
nen AC<BE
            d_ xet tam giac AEB ta co
EK la duong cao, ( EK vuong foc AB)
BD la duong cao ( BD vuong foc AE
AC la duong cao ( AC vuong goc BC )
==> EK,BD,AC dong quy tai 1 die

:3