Question

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

Answer 1

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.

Answer 2

Hello mate ^_^

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$\bold\pink{Solution:}$

AB=AC         (Given)

It means that ∠DBC=∠ACB           (In triangle, angles opposite to equal sides are equal)     

Let ∠DBC=∠ACB=x         .......(1)

AC=AD          (Given)

It means that ∠ACD=∠BDC         (In triangle, angles opposite to equal sides are equal)     

Let ∠ACD=∠BDC=y           ......(2)

In ∆BDC, we have

∠BDC+∠BCD+∠DBC=180°     (Angle sum property of triangle)

⇒∠BDC+∠ACB+∠ACD+∠DBC=180°

Putting (1) and (2) in the above equation, we get

y+x+y+x=180°

⇒2x+2y=180°

⇒2(x+y)=180°

⇒(x+y)=180/2=90°

Therefore, ∠BCD=90°

hope, this will help you.☺

Thank you______❤

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