Question

Cho \(\Delta\)ABC,AB=AC.Vẽ phía ngaofi \(\Delta\)ABC các tam giác vuông \(\Delta\)ABK và \(\Delta\)ACD có AB=AK,AC=AD.CM \(\Delta\)ABK=\(\Delta\)ACD

Answer 1

Giải:
Ta có: AB = AC

           AB = AK

           AC = AD

=> AD = AK (1)

Xét \(\Delta ABK\) có: \(\widehat{BAK}=\widehat{BAC}+\widehat{A_2}=\widehat{BAC}+90^o\)

Xét \(\Delta ACD\) có: \(\widehat{DAC}=\widehat{BAC}+\widehat{A_1}=\widehat{BAC}+90^o\)

\(\Rightarrow\widehat{BAK}=\widehat{DAC}\left(=\widehat{BAC}+90^o\right)\)(2)

Xét \(\Delta ABK,\Delta ACD\) có:

\(AB=AC\left(gt\right)\)

\(\widehat{BAK}=\widehat{DAC}\) ( theo (2) )

\(AD=AK\) ( theo (1) )

\(\Rightarrow\Delta ABK=\Delta ACD\left(c-g-c\right)\) ( đpcm )