Question

In triangle abc if ab=ac and ad is median then angle adc =to

Answer 1

CONSIDER triangle ADB and triangle ADC
AD = AD ( common)
AB=AC (given)
BD = CD ( because AD is a median)
We can say triangle ADB and triangle ADC are congruent by SSS congruency


As angle ADB and angle ADC are equal by cpct
And we know BC is straight line
Angle ADB + Angle ADC = 180

both are 90

Hence ANGLE ADC IS 90 DEGREES

Answer 2

Given :  ∆ABC   is an isosceles triangle such that AB = AC and

AD is median to BC.

To Find : ∠adc  

Solution:

∆ BAD  and ∆  CAD  

AB = AC    Given

AD = AD    Common

BD = CD  = BC/2  as AD is the median

Using side - side - side congruence property

∆ BAD  ≅ ∆  CAD  

=> ∠ADC ≅ ∠ADB

AB is straight line

Hence  ∠ADC and  ∠ADB form a linear pair

=> ∠ADC +   ∠ADB = 180°

=> 2∠ADC  =  180°

=>∠ADC  = 90°

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