using the segment addition postulate, which is true?\na b c d\n-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8…

using the segment addition postulate, which is true?\na b c d\n-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9\nab + bc = ad\nab + bc = cd\nbc + cd = ad\nbc + cd = bd

using the segment addition postulate, which is true?\na b c d\n-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9\nab + bc = ad\nab + bc = cd\nbc + cd = ad\nbc + cd = bd

Answer

Explanation:

Step1: Recall Segment Addition Postulate

The segment addition postulate states that if three points ( B ), ( C ) are on a line segment ( BD ) such that ( C ) is between ( B ) and ( D ), then ( BC + CD = BD ).

Step2: Analyze the Number Line

From the number line:

  • Point ( B ) is at (-1), ( C ) is at ( 2 ), ( D ) is at ( 8 ).
  • Check the positions: ( B ), ( C ), ( D ) are colinear with ( C ) between ( B ) and ( D ).

Step3: Evaluate Each Option

  • Option 1: ( AB + BC = AD ). ( AB ) is from ( A(-6) ) to ( B(-1) ) (length ( 5 )), ( BC ) is from ( B(-1) ) to ( C(2) ) (length ( 3 )), ( AD ) is from ( A(-6) ) to ( D(8) ) (length ( 14 )). ( 5 + 3 = 8 \neq 14 ).
  • Option 2: ( AB + BC = CD ). ( AB + BC = 5 + 3 = 8 ), ( CD ) is from ( C(2) ) to ( D(8) ) (length ( 6 )). ( 8 \neq 6 ).
  • Option 3: ( BC + CD = AD ). ( BC + CD = 3 + 6 = 9 ), ( AD = 14 ). ( 9 \neq 14 ).
  • Option 4: ( BC + CD = BD ). ( BC = 3 ), ( CD = 6 ), ( BD ) is from ( B(-1) ) to ( D(8) ) (length ( 9 )). ( 3 + 6 = 9 ), which matches.

Answer:

D. ( BC + CD = BD )