Question

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

Explanation:

Step1: Recall midpoint definition

If \( A \) is the midpoint of \( SM \), then \( SA = AM \) and \( SA + AM = SM \) (by segment addition postulate, the sum of two adjacent segments equals the whole segment).

Step2: Analyze each equation

• For \( SA = AM \): Since \( A \) is the midpoint, this is true.
• For \( SM + AM = SA \): \( SM \) is the whole segment, \( AM \) is a part, so \( SM+AM>SA \), this is false.
• For \( AM + SM = SA \): Similarly, \( AM + SM>SA \), this is false.
• For \( SA + AM = SM \): By segment addition, this is true as \( SA \) and \( AM \) are parts of \( SM \).

Answer:

• \( SA = AM \)
• \( SM + AM = SA \) (This is incorrect, correct should be \( SA + AM = SM \))
• \( AM + SM = SA \) (This is incorrect, correct should be \( SA + AM = SM \))
• \( SA + AM = SM \)