Question

If ab=bc and ao=cq than proves that bp=bq

Answer 1

here is your answer

first method

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

second method

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