# In a line segment, segment AC = segment BD. Fill in the reasons to prove segment CD is congruent to segment AB. Statements: Reason:...

In a line segment, segment AC = segment BD. Fill in the reasons to prove segment CD is congruent to segment AB.

Statements: Reason:

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.

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### 1 Answer

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.

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