Question

use the picture to write the correct segment addition statement. image: line segment with points a, b, c (a---b----c). options: ba + ac = bc; ab + bc = ab; ab + bc = ac; bc + ba = bc

Explanation:

Step1: Recall Segment Addition Postulate

The Segment Addition Postulate states that if a point \( B \) is between points \( A \) and \( C \), then \( AB + BC = AC \).

Step2: Analyze the Diagram

In the given diagram, point \( B \) lies between points \( A \) and \( C \) on the line segment \( AC \). So, the length of \( AB \) plus the length of \( BC \) should equal the length of \( AC \).

Step3: Evaluate the Options

• Option 1 (\( BA + AC = BC \)): Incorrect, as \( BA \) is same as \( AB \), and \( AB + AC \) would be longer than \( BC \).
• Option 2 (\( AB + BC = AB \)): Incorrect, as \( AB + BC \) should be \( AC \), not \( AB \).
• Option 3 (\( AB + BC = AC \)): Correct, follows the Segment Addition Postulate.
• Option 4 (\( BC + BA = BC \)): Incorrect, as \( BC + BA \) (same as \( BC + AB \)) should be \( AC \), not \( BC \).

Answer:

C. \( AB + BC = AC \) (assuming the orange option is labeled C, as per the order: yellow, purple, orange, teal corresponding to options 1 - 4, and the correct one is the orange one with \( AB + BC = AC \))