Question

Triangle abc is isosceles triangle ab = ac side ba produced to d such that ad equal a b show angle bcd is equals to 90 degree

Answer 1

given:- Triangle ABC is a isosceles triangle
2.) AB = AC
To prove:- AB=AC (given)
AD=DA ( common)
BD= AD ( bcz AD is a median so the bisect the line BC into two equal parts)
therefore triangle ADB ~ ADC ( by SSS congruence rule). - (equation 1st)

Now,
ADC + ADB = 180°
ADC +ADC= 180°. ( we proved the angle ADC = ADB in equation 1st so we written as ADB is ADC)
2ADC= 180°
ADC=180÷2 =90°. (equation 2nd)

we proved in equation 2nd ADC is 90° and we proved in equation 1st ADC = ADB there for ADB is also 90° (H.P)

Answer 2

Hello mate ^_^

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$\bold\green{Solution:}$

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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