using the segment addition postulate, which is true?\nab + bc = ad\nab + bc = cd\nbc + cd = ad\nbc + 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\neq AD = 16)
• Option 2: (AB + BC=8+3 = 11\neq CD=5)
• Option 3: (BC + CD=3 + 5=8\neq AD = 16)
• Option 4: (BC+CD=3 + 5=8) and (BD = 8)

Answer:

(BC + CD=BD)