Question

ABC is an isosceles triangle with AB = AC and D is a point of BC. such that AD perpendicular BC. prove that angle BAD= angle CAD.​

Answer 1

Answer:

see above picture....

Answer 2

Given : ABC is an isosceles triangle with AB = AC and D is a point on BC such that ad is perpendicular to BC  

To find : Show that  ∠BAD =  ∠CAD

Solution:

AD ⊥  BC

=> ΔABD  & ΔACD are right angle triangle

Applying Pythagorean theorem

BD² = AB² - AD²

AB = AC

=> BD² = AC² - AD²

AC² - AD²  = CD²

=> BD² =  CD²

=> BD = CD  Eq 1

Compare ΔABD  & ΔACD

AB = AC  ( given)

BD = CD   ( from Eq 1)

AD = AD   ( common)

=>  ΔABD  ≅ ΔACD

=> ∠BAD =  ∠CAD

QED

Hence proved

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