Q. 63.9( 472 Votes )

ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that BCD is a right angle.


Answer :

Given: AB = AC and AD = AB
To Prove: ∠ BCD is a right angle

Proof: In  

AB = AC (Given)


ACB = ABC (Angles opposite to equal sides are equal)


In


AD = AB     (Given)


ADC = ACD (Angles opposite to equal sides are equal)


Now,


In


CAB + ACB + ABC = 180o            ( Sum of interior angles of a triangle)


CAB + 2 ACB = 180                   (∠ACB = ∠ABC)


CAB = 180o - 2 ACB (i)


Similarly,

In

CAD = 180o - 2 ACD (ii)


Also,


CAB + CAD = 180o                    (BD is a straight line)


Adding (i) and (ii), we get


CAB + CAD = 180o - 2ACB + 180o - 2ACD


180o = 360o - 2ACB - 2ACD


2 (ACB + ACD) = 180o


BCD = 90o
Hence, Proved.

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