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

Question

Geometry proofs help!!!

Answer 1

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