Question

in triangle abc angle=90 degree ab=ac bisector of angle A meet BC at D prove that BC=2AD

Answer 1

answer in the picture.

Answer 2

Given:- In triangle ABC, angle A is 90°. AD is the inspector of angle A. AB = AC.
To prove :- BC = 2AD
Proof :-
In triangle ADB and ADC,
I) AB = AC (given)
II) angle DAB = angle CAD (given)
III) AD = AD (common)
Therefore by SAS criteria,
Triangle ADB is congurent to triangle ACD.
BT CPCT, we get BD = CD.
angle ADB = angle ADC
but these are linear pairs
So, angle ADB+ angle ADC = 180°
or, angle ADB + angle ADB = 180° (from above)
or, 2 angle ADB = 180°
or, angle ADB = 90°

Therefore angle ADB = ADC = 90°
In triangle ADB,
angle ADB +BAD + DBA = 180°
or, BAD + DBA = 180° - 90°
or, 45° + DBA = 90°
or, DBA = 45°
As DBA & BAD = 45°
so, Triangle ADB is an isoceleus triangle