Question

Cho tam giác ABC có AC> AB, góc B > góc  C
a) Vẽ phân giác AD (D thuộc BC). Chứng minh góc ADC > góc ADB

Answer 1

a: \(\widehat{BAD}+\widehat{B}+\widehat{ADB}=\widehat{CAD}+\widehat{C}+\widehat{ADC}\left(=180^0\right)\)

\(\Leftrightarrow\widehat{B}+\widehat{ADB}=\widehat{C}+\widehat{ADC}\)

mà \(\widehat{B}>\widehat{C}\)

nên \(\widehat{ADB}< \widehat{ADC}\)

Answer 2

a, Ta có ^ADC = 180⁰ - ^C - ^DAC 

^ADB = 180⁰ - ^B - ^BAD 

mà ^DAC = ^BAD ( AD là pg ) 

^B > ^C (gt) 

=> ^ADC > ^ADB