Question

Name or state the postulate, definition, or theorem that justifies each statement about the diagram.

$AE+EC=AC$.

Short answer

The postulate that justifies the given statement is the Segment Addition Postulate.

Step-by-step solution

Step 1. Find the suitable line segments.

Observe that the three points A,E, C are collinear, and E lies between the line joining of Aand C .

Step 2. Determine the theorem or postulate that can be used.

Postulate 2, the Segment Addition Postulate, states that if B is between A and C, then $AB+BC=AC$.

Step 3. Use the postulate.

By using segment addition postulate, the statement $AE+EC=AC$is justified_.