Q. 54.3( 31 Votes )

ABC is an isoscel

Answer :

Given:- AB=AC and ABC is isosceles triangle


QAD= DAC


CD||BA


Formula used:- sum of angles of triangle is 180°


Solution:-


As Δ ABC is a isosceles triangle


ABC= ACB


ABC+ ACB+ CAB=180°


2 ACB+ CAB=180°


*As BAQ is a straight line


CAB+ DAC+ QAD=180°


* QAD= DAC [Given]


CAB=180° - 2 DAC


Putting value of CAB in above equation 1


2 ACB+180° - 2 DAC=180°


2 ACB =2 DAC


ACB = DAC


If;


There is ACB = DAC and AC is the transverse


these are equal by alternate angles


And AD||BC


In ABCD


If;


AD||BC & CD||BA


If both pair of sides of quadrilateral are parallel


Then the quadrilateral is parallelogram


Conclusion:-


ABCD is a parallelogram


And DAC = BCA


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