Question

1. given: ( ab ) and ( cd ) bisect each other at point ( m ) and ( bm = cm ).

prove: ( ab = am + dm )
( bm = dm )
( ab = am + bm )
( bm = cm )
( cm = dm )
choices
given
definition of bisect
transitive property
segment addition postulate

Explanation:

Step1: BM = DM

Since \(AB\) and \(CD\) bisect each other at point \(M\), by the definition of bisect, \(CM = DM\) and \(AM=BM\).

Step2: AB = AM + BM

By the Segment Addition Postulate, for collinear points \(A\), \(M\), and \(B\), \(AB=AM + BM\).

Step3: BM = CM

Given in the problem statement.

Step4: CM = DM

Since \(AB\) and \(CD\) bisect each other at point \(M\), by the definition of bisect.

Answer:

\(BM = DM\): Definition of bisect; \(AB = AM + BM\): Segment Addition Postulate; \(BM = CM\): Given; \(CM = DM\): Definition of bisect.