in a triangle abc ab =ac,ba is produced to d and ae is drawn parallel to bc ,prove that ae - Maths - Triangles

Question

in a triangle abc ab =ac,ba is produced to d and ae is drawn
parallel to bc ,prove that ae bisects angle dac

Neha Sethi · Accepted Answer

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Given △ABC, AB=ACAE∥BC⇒∠3=∠2  
1  alternate interior anglesNow, ∠3+∠4=∠1+∠2  exterior angle property⇒∠2+∠4=∠1+∠2   using 1⇒∠4=∠1   
2But ∠1=∠2   angles opposite to equal sides AB=AC are equal
⇒∠1=∠2=∠3   using 1⇒∠1=∠3  
3From 2 and 3, we get∠3=∠4⇒AE bisects ∠DAC

in a triangle abc ab =ac,ba is produced to d and ae is drawn parallel to bc ,prove that ae bisects angle dac