Abc is an isosceles triangle with ab ac

Asked by admin @ 24/08/2021 in Math viewed by 277 People

ABC is an isosceles triangle in which AB=AC.Side BA is produced to D Such that AD=AB.Show that BCD is a right angled triangle

Answered by admin @ 24/08/2021

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.

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