Geometry proofs help!!!

## Given: line ae is congruent to line bd, line cd is congruent to line ce prove: line ac is congruent to line bc

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# 1 Answer

Liz,

First, generally, "lines" cannot be described as congruent because they have no definite length, so I think you are describing line segments. Line segments are congruent if their lengths are equal.

Second, I think there is information in your picture that is not being conveyed in the text of the question. I suspect that your picture might look something like this

A B

\ /

\ /

\ /

\ /

C

/ \

/ \

/ \

/ \

D E

So a two line proof of this using this figure might look something like this

1. AE ≅ BD Given

2. CD ≅ CE Given

3. AE = BD Def. of congruent segments

4. CD = CE Def. of congruent segments.

5. AE = AC + CE Whole is equal to the sum of its parts

6. BD = BC + CD Whole is equal to the sum of its parts

7. AC + CE = BC + CD Substitution lines 3, 5 & 6

8. AC + CD = BC + CD Substitution lines 4 & 7

9. AC = BC Subtracting CD from both sides of line 8 (Equals subtracted by equals are equal).

10. AC ≅ BC Def. of congruent segments.

The key points to take away from such a proof are to (1) understand relationship between congruence and equality of measure and (2) unpack information from definitions and postulates. Stay warm, and I hope this was helpful. John