Question

precision if point p is between a and m, select the true statement

a) ( am = am + mp )
b) ( pm = ap )
c) ( ap + pm = am )
d) ( am + ap = pm )

Explanation:

Step1: Analyze Option A

If \(AM = AM+MP\), then \(0 = MP\) which is not necessarily true.

Step2: Analyze Option B

\(PM = AP\) would mean \(P\) is the mid - point of \(AM\), but we are only told \(P\) is between \(A\) and \(M\), not that it is the mid - point.

Step3: Analyze Option C

By the segment addition postulate, if \(P\) is between \(A\) and \(M\), then \(AP + PM=AM\).

Step4: Analyze Option D

If \(AM + AP=PM\), then \(AM=PM - AP\). But by the segment addition postulate \(PM=AM - AP\) (when \(P\) is between \(A\) and \(M\)), so this is incorrect.

Answer:

C. \(AP + PM = AM\)