Question
Tue September 08, 2009 By:

prove that

Expert Reply
Wed September 09, 2009

Given: ABC is an isoceles triangle with AB = AC

AD = AB

To prove: BCD = 900

Proof: AB = AC   ...(1)

ABC = ACB     (angle opposite to equal sides)

we have, AD = AB

⇒ AD = AC     (from (1))

ACD = ADC    (angle opposite to equal sides)

Let ABC = ACB = ACD = ADC = x

Now in BDC

By angle sum property,

DBC + DCB + BDC = 1800

DCB = DCA+ACB = x+x = 2x

So, DBC + DCB + BDC = x + 2x + x =1800

⇒ x = 450

Therefore, BCD = 900

x+

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