Question

triangle 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 angle.
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Answer 1

Answer:

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Step-by-step explanation:

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