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

• \(AB=\vert-1-(-6)\vert = 5\)
• \(BC=\vert2 - (-1)\vert=3\)
• \(CD=\vert8 - 2\vert = 6\)
• \(AD=\vert8-(-6)\vert = 14\)
• \(BD=\vert8-(-1)\vert=9\)

Step2: Check each option

• For \(AB + BC\): \(5 + 3=8

eq14(AD)\)

• For \(AB + BC\): \(5+3 = 8

eq6(CD)\)

• For \(BC + CD\): \(3+6=9

eq14(AD)\)

• For \(BC + CD\): \(3 + 6=9 = BD\)

By the segment - addition postulate (if \(B\) is between \(A\) and \(C\), then \(AB+BC = AC\)), for points \(B\), \(C\), \(D\), if \(C\) is between \(B\) and \(D\), then \(BC + CD=BD\)

Answer:

BC + CD = BD