Question

Q-10. AABC is an isosceles triangle in which AB=AC. Side BA is produced to D such that
AD=AB. Show that ZBCD is right angle.

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Answer 1

Answer:

AB = AD

AB = AC

SO, AC = AD

In triangle ABC,

BCA = ABC ........1

In triangle ADC,

ACD = CDA .......2

From 1 and 2 we get,

BCA + ACD = ABC + CDA

or, BCD = ABC + CDA ......3

Now,

BCA + ABC + CDA = 180°[sum of all angles]

or, BCA + BCA = 180°[From 3]

or, 2BCA = 180°

or, BCA = 90°

Therefore BCD is a right angled triangle....

Proved.