Question

select all the equations that satisfy this fact. in the figure shown, a is the mid - point of sm. sm+am = sa sa = am sa+am = sm am+sm = sa

Explanation:

Step1: Recall mid - point property

If \(A\) is the mid - point of \(\overline{SM}\), then \(SA = AM\) and \(SA+AM = SM\) because the whole segment \(\overline{SM}\) is composed of two equal sub - segments \(\overline{SA}\) and \(\overline{AM}\).

Step2: Analyze each equation

For \(SM + AM=SA\), since \(SM=SA + AM\), then \(SA+AM+AM
eq SA\), so this equation is incorrect.
For \(SA = AM\), this is correct by the definition of a mid - point.
For \(SA + AM=SM\), this is correct as the sum of two sub - segments of a line segment equals the whole line segment.
For \(AM + SM=SA\), since \(SM = SA+AM\), then \(AM+(SA + AM)
eq SA\), so this equation is incorrect.

Answer:

\(SA = AM\), \(SA + AM = SM\)