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abc is a triangle and ab=bc and bp-bq show that ap=cq using euclids axiom or postulates.

AB=AC
AP+BP=AQ+CQ

(BY AXIOM 3 THINGS WHICH R EQUAL TO ONE ANOTHER IS EQUAL TO ONE ANOTHER)

AP+BP-BP=AQ+CQ-AQ
AP=CQ

HENCE PROVED
 
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AB=BC i.e.,AP+BP=CQ+BQ BP=BQ (given) According to the axiom anything that is equal to the same thing is equal to one another Hence we can conclude that AP=CQ
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In triangle ABC
AB=BC (GIVEN)
AP=CQ  (GIVEN)
AP+BP=CQ  accoding to the euclid's [1] axiom things which are equal to the same thing are equal to one another
Hence proved that BP=BQ




​HOPE THIS SOLUTION HELPS U
 
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