Answer:
1. AC+BD given.
2. AC=AB+BC; Segment addition postulate.
4. AB+BC=BC+CD; Substitution property of equality.
Step-by-step explanation:
We have been given a line segment AD with points A B C and D sitting on AD from left to right and we are asked to find the reasons for given statements.
1. AC=BD is given. Therefore, we will add 'given' in first reason box.
2. We know If two points (A and C) lies on a line segment and third point (B) lies between these points then by segment addition postulate the distance between AC will be equal to sum of distances between AB and BC.
4. Since we know that substitution property of equality states that if x=y than we can substitute x in place of y in any equation and y in place of x as well in any equation. Since we know that [tex]AC=AB+BC[/tex] and [tex]BD=BC+CD[/tex]
Therefore, by substitution property of equality [tex]AB+BC=BC+CD[/tex].
