Question

angle a is 90 degree im triangle abc and ab=ac.The bisector of angle a meet bc at d.Prove that bc= 2ad​

Answer 1

Answer 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