In isosceles triangle ABC- AB- AC- The side BA is produced to D such that BA- AD- Hence- - BCD- 90-If the above statement is true then mention answer as 1- else mention 0 if false

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Angle Sum Property

In isosceles ...

Question

In isosceles triangle $A B C$ , $A B = A C$ . The side $B A$ is produced to $D$ such that $B A = A D$ .
Hence, $∠ B C D = 90^{\circ}$
If the above statement is true then mention answer as 1, else mention 0 if false

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Solution

In triangle ABC,
AB = AC, so , $∠ A B C = ∠ A C B$
Now, since, AB =AD then, AC = AD
hence, $∠ A C D = ∠ A D C$
Now, let $∠ A B C = ∠ A C B = x$ and $∠ A C D = ∠ A D C = y$
so, $∠ A B C + ∠ B C D + ∠ B D C = 180$
$∠ A B C + ∠ A C B + ∠ A C D + ∠ B D C = 180$
$x + x + y + y = 180$
$2 (x + y) = 180$
$x + y = 90$
$∠ A C B + ∠ A C D = 90$
$∠ B C D = 90$

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In isosceles triangle ABC, AB=AC. The side BA is produced to D such that BA=AD. Hence, ∠BCD=90∘If the above statement is true then mention answer as 1, else mention 0 if false

In triangle ABC,AB = AC, so , ∠ABC=∠ACBNow, since, AB =AD then, AC = ADhence, ∠ACD=∠ADCNow, let ∠ABC=∠ACB=x and ∠ACD=∠ADC=yso, ∠ABC+∠BCD+∠BDC=180∠ABC+∠ACB+∠ACD+∠BDC=180x+x+y+y=1802(x+y)=180x+y=90∠ACB+∠ACD=90∠BCD=90

In isosceles triangle $A B C$ , $A B = A C$ . The side $B A$ is produced to $D$ such that $B A = A D$ .
Hence, $∠ B C D = 90^{\circ}$
If the above statement is true then mention answer as 1, else mention 0 if false