Question

prove that;
1- ∆abd =∆ acd
2- angle b = angle c
3- angle adb = angle ADC
4- angle adb = 90°

Answer 1

In triangle ADC and triangle ADB
AB=AC (given)
AD=AD(common)
BD=DC(given)
therefore triangle ADC= triangle ADB (SSS)
so angle b= angle c (cpct)
so angle ADB= angle ADC (cpct)
since AD is perpendicular on BC
therefore AD=90