Question

∆Abc is a isosceles triangle in which ab = ac. side ba produced d such that ad...
right answer
no spam​

Answer 1

Answer:

Question ::

➡️∆ABC is a isosceles triangle in which AB = AC. side BA produced to D such that AD=AB.Show that angle BCD is a right angle triangle.

Answer::

➡️Consider ∆ABC,

ABC, It is given that AB = AC

So,

(Since angles opposite to the equal sides are equal.)

∠ABC= ∠ACB...........................(i)

AB=AC and AD=AB

So AC=AD

Similarly in ∆ACD,

∠CDA= ∠ACD

SO ∠CDB= ∠ACD......................(ii)

Adding (i) and (ii), we get :

∠ABC+ ∠CDB= ∠ACB+ ∠ACD

∠ABC+ ∠CDB=∠BCD................(iii)

In ∆BCD,

∠BCD+∠DBC+∠CDB=180°

=>∠BCD+∠ABC+∠CDB=180°

From iii

∠BCD+∠BCD=180°

So ∠BCD=90°

➡️Hence proved