The angle bisectors of an equilateral triangle ABC meet at a point P .Prove that triangle BCP, triangle ABP ,triangle ACP are congruent

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Please find below the solution to the asked query :



As ABC is an equilateral So,A=B=C=60°Now,AP , BP and CP are angle bisectors .So,ABP=PBC=PCB=PCA=PAC=PAB=30°Now,In ABP and BCPAB=BC    Sides of equilateral triangleABP=BCP=30°PAB=PBC=30°By ASA congruency criterionABP  BCP   ... 1Now,In BCP and ACPBC=AC    Sides of equilateral triangleBCP=ACP=30°PBC=PAC=30°By ASA congruency criterionBCP  ACP   ... 2From 1 and 2ABP  BCP  ACPHence Proved.
 
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