# Geometry Proofs Help

1. ### ccseagle

24
Geometry Proofs.. Help!!

Please please someone help me!! I have a Geometry Exam on :surprised Monday and I don't understand proofs one bit !! If someone could help me with a few proofs that would be so awesome!!

2. ### cristo

8,384
Staff Emeritus
Have you got any specific questions?

3. ### ccseagle

24
yeah, could you help me with this proof..

Given: B is between A and C; D is between C and E; and C is the midpoint of line BD and of line AE

Prove: line AB is congruent to line DE

Picture:

<--A---B---C---D---E-->

4. ### ccseagle

24
yeah, could you help me with this proof..

Given: B is between A and C; D is between C and E; and C is the midpoint of line BD and of line AE

Prove: line AB is congruent to line DE

Picture:

<--A---B---C---D---E-->

5. ### cristo

8,384
Staff Emeritus
Ok, I'll give a hint. You know that $$|\vec{AC}|=|\vec{CE}|$$ so start with this, then express both sides of the equation in terms of two new lengths. Have a go, and post your thoughts.

6. ### ccseagle

24
AB+BC= line AC

and

CD+CE = line CE

I don't know, am I even on the right track??

7. ### cristo

8,384
Staff Emeritus
Yes, so now the equation becomes:$$|\vec{AC}|=|\vec{CE}| \Rightarrow |\vec{AB}|+|\vec{BC}|=|\vec{CD}|+|\vec{DE}|$$ Carry on with this.

8. ### ccseagle

24
umm.. would the reason be substitution??

9. ### ccseagle

24
Line AC is congruent to line CE??

10. ### cristo

8,384
Staff Emeritus
Ok, my notation
means that the length of the line AC is equal to the length of the line CE (this is equivalent to the two lines being congruent).

We know that AC is congruent to CE, since C is the midpoint of AE. CAn you say anything similar regarding the lines BC and CD

11. ### ccseagle

24
C is the midpoint of lines BC and CD?

12. ### cristo

8,384
Staff Emeritus
WEll, C is the midpoint of BD, therefore BC and CD are congruent. Now look at the equation given in post #7. What does this tell you?

13. ### ccseagle

24
I don't think I understand.. Can you give me a hint??

14. ### cristo

8,384
Staff Emeritus
Not without giving you the answer!! Ok, here goes: The equation can be rearranged to give

$$|\vec{AB}|-|\vec{DE}| =|\vec{CD}|-|\vec{BC}|$$
Now, since the BC and CD are congruent, what can say about the RHS of the equation? What does this then imply?

15. ### ccseagle

24
I don't know.. Umm whats a RHS??

16. ### cristo

8,384
Staff Emeritus
Right hand side. Ok, if two lines are congruent, then it means they have the same length. Lets call this length x. Then the RHS is x-x=...?

17. ### ccseagle

24
the lengths are congruent?

18. ### cristo

8,384
Staff Emeritus
Well, $$|\vec{AB}|-|\vec{DE}| =|\vec{CD}|-|\vec{BC}|=0 \Rightarrow |\vec{AB}|=|\vec{DE}|$$

And so, the lines AB and DE are congruent.

19. ### ccseagle

24
Ok, i think i get it.. Thanks.. Do you think you could help me with a couple more??

20. ### cristo

8,384
Staff Emeritus
Maybe one, it's getting quite late. Post your attempt at a proof to the problem you post first though.