Question

using the segment addition postulate, which is true?
ab + bc = ad
ab + bc = cd
bc + cd = ad
bc + cd = bd

Explanation:

Step1: Calculate the length of each segment

The length of a segment with endpoints \(x_1\) and \(x_2\) on the number - line is \(|x_2 - x_1|\).
For segment \(AB\): If \(A=-6\) and \(B = - 1\), then \(AB=|-1-(-6)|=|-1 + 6|=5\).
For segment \(BC\): If \(B=-1\) and \(C = 2\), then \(BC=|2-(-1)|=|2 + 1|=3\).
For segment \(CD\): If \(C = 2\) and \(D = 8\), then \(CD=|8 - 2|=6\).
For segment \(AD\): If \(A=-6\) and \(D = 8\), then \(AD=|8-(-6)|=|8 + 6|=14\).
For segment \(BD\): If \(B=-1\) and \(D = 8\), then \(BD=|8-(-1)|=|8 + 1|=9\).

Step2: Check each option

• Option 1: \(AB + BC=5 + 3=8

eq AD = 14\).

• Option 2: \(AB + BC=5+3 = 8

eq CD=6\).

• Option 3: \(BC + CD=3 + 6=9

eq AD = 14\).

• Option 4: \(BC+CD=3 + 6=9\) and \(BD = 9\).

Answer:

\(BC + CD=BD\)