Question

ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠ BCD is a right angle.
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Answer 1

Solution :

In ABC

( angle opposite to equal sides are equal )

so

Abc = Abc

In ABC

AD = Ab

/ Acd = / AcD

So now ,

In /\ Abc

/ Cab + / Abc + / Abc = 180 op2

/ Cab + 2 / Abc = 180 o

/ Cab = 180 o - 2 / Acb (i)

In.

/ Cad = 180 - 2 / Acd (ii)

So,

/ Cab + / Cad = 180o

Adding (i) and ( ii)

/ Cab + / Cad = 180 o - 2 / Acb + 180o - 2 / Acd

180o = 36o - 2 / Acb - 2 / Acd

2 / Abc + / Acd = 180o

So ,

180° = 90°

2

So ANSWER is = 90°

Thanks .

Answer 2

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