In a line segment, segment AC = segment BD. Fill in the reasons to prove segment CD is congruent to segment AB.
1.Segment AC = segment BD 1._____ I think this would be "given"
2. AC= AB +BC 2.__ (I think this is segment addition postulate)
3. AB+BC=BD 3.__ (I think this is segment addition postulate)
4. BD=BC+CD 4._(I think this is substitution property of equality)
5. AB+BC=BC+CD 5._ (I think this is addition property of equality)
6. AB = CD 6._ (I think this is subtraction property of equality)
7.CD=AB 7. (I think this is symmetric property of equality)
8.CD is congruent to AB 8. (I think this would be definition of congruent segments)
Thank you for your help.
Line segments are congruent if they have the same length.
Draw a straight line AD. Take two points B and C in between A and D such that points A, B, C, and D appear in a sequence, say from left.
Given segment AC = segment BD ---- (i)
Again, Splitting AC and BD in terms of further segments, we can write
AC = AB + BC and similarly, BD = BC + CD
Therefore, applying addition property in equality (i) it follows that,
AB + BC = BC + CD
`rArr` AB = CD (subtracting the common part BC from both sides)
Thus, option 5) should be the reason for congruence of AB and CD.