Question

Suppose ABC is an isosceles triangle with AB = AC. Side BA is produced to D such that BA = AD. Prove that ∠BCD is a right angle.

Answer 1

therefore c = 90 - X + x

Answer 2

Given ∆ABC is an Isosceles triangle .

AB = AC

BA is produced to D such that

BA = AD

Now ,

i ) In ∆ABC ,

AB = AC ,

<ABC = <ACB = x -----( 1 )

[ Angles opposite to equal sides ]

ii ) In ∆DAC ,

BA = AD = AC

<ACD = <BDC = y ----( 2 )

[ Angle opposite to equal sides ]

iii ) In ∆BCD ,

<DBC + <BCD + <BDC = 180°

[ Angle sum property ]

=> x + ( x + y ) + y = 180°

=> 2x + 2y = 180°

Divide each term by 2 , we get

=> x + y = 90°


=> <BCD = x + y = 90°

Therefore ,

<BCD is a right angle .

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