Question

cho tam giac ABC vuong tai A co B= 30

a, tinh C

b, ve tia phan giac goc C cat canh AB tai D. tren canh CB lay diem Msao cho CA=CM. chung minh ΔACD=ΔMCD

c, qua C ve duong thang xy vuong goc voi CA. tu A ke duong thang song song voi CD cat xy o K. cm AK=CD

d, tinh goc AKC

Answer 1

a,\(\widehat{C}=180^o-90^o-\widehat{B}=90^o-30^o=60^o\)

b, Xét \(\Delta ACD-vs-\Delta MCD\)

- AC = CM (gt)

- \(\widehat{ACD}=\widehat{MCD}\) (gt)

- CD chung (gt)

=> \(\Delta ACD=\Delta MCD\left(c-g-c\right)\)

c, Ta có:

AK // CD và CK // AD => AK = CD (t/c đoạn chắn)

d, \(\left\{{}\begin{matrix}\widehat{BAC}=\widehat{ACK}=90^o\\\widehat{ACD}=\widehat{CAK}=\dfrac{1}{2}\widehat{C}=30^o\left(so-le-trong\right)\end{matrix}\right.\Rightarrow\widehat{ADC}=\widehat{AKC}=180^o-90^o-30^o=60^o\)