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

Let's assume each unit on the number - line is 1.

• For segment \(AB\): If \(A=- 9\) and \(B = - 1\), then \(AB=\vert-1-(-9)\vert=\vert-1 + 9\vert = 8\)
• For segment \(BC\): If \(B=-1\) and \(C = 2\), then \(BC=\vert2-(-1)\vert=\vert2 + 1\vert=3\)
• For segment \(CD\): If \(C = 2\) and \(D=7\), then \(CD=\vert7 - 2\vert=5\)
• For segment \(AD\): If \(A=-9\) and \(D = 7\), then \(AD=\vert7-(-9)\vert=\vert7 + 9\vert=16\)
• For segment \(BD\): If \(B=-1\) and \(D = 7\), then \(BD=\vert7-(-1)\vert=\vert7 + 1\vert=8\)

Step2: Check each option

• Option 1: \(AB + BC=8 + 3=11

eq AD = 16\)

• Option 2: \(AB + BC=8+3 = 11

eq CD=5\)

• Option 3: \(BC + CD=3 + 5=8

eq AD = 16\)

• Option 4: \(BC+CD=3 + 5=8\) and \(BD = 8\)

Answer:

\(BC + CD=BD\)