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

• For \(AB\): \(A=-6\), \(B = - 1\), so \(AB=\vert-1-(-6)\vert=\vert-1 + 6\vert = 5\)
• For \(BC\): \(B=-1\), \(C = 2\), so \(BC=\vert2-(-1)\vert=\vert2 + 1\vert=3\)
• For \(CD\): \(C = 2\), \(D = 8\), so \(CD=\vert8 - 2\vert=6\)
• For \(AD\): \(A=-6\), \(D = 8\), so \(AD=\vert8-(-6)\vert=\vert8 + 6\vert=14\)
• For \(BD\): \(B=-1\), \(D = 8\), so \(BD=\vert8-(-1)\vert=\vert8 + 1\vert=9\)

Step2: Check each option

• Option1: \(AB + BC=5 + 3=8

eq AD = 14\)

• Option2: \(AB + BC=5+3 = 8

eq CD=6\)

• Option3: \(BC + CD=3 + 6=9

eq AD = 14\)

• Option4: \(BC+CD=3 + 6=9\), and \(BD = 9\)

Answer:

\(BC + CD=BD\) (the fourth option)