Question

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

o a) am = am + mp

o b) pm = ap

o c) ap + pm = am

o d) am + ap = pm

Explanation:

Step1: Analyze Option A

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

Step2: Analyze Option B

\(PM = AP\) would mean \(P\) is the mid - point, but there is no information given to suggest that \(P\) 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 \(PM=AM - AP\) (rearranged \(AP + PM = AM\)), so this is incorrect.

Answer:

C. \(AP + PM = AM\)