# Geometry Proofs Help

#### ccseagle

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!!

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#### cristo

Staff Emeritus
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!!
Have you got any specific questions?

#### ccseagle

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-->

#### ccseagle

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-->

#### cristo

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.

#### ccseagle

AB+BC= line AC

and

CD+CE = line CE

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

#### cristo

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.

#### ccseagle

umm.. would the reason be substitution??

#### ccseagle

Line AC is congruent to line CE??

#### cristo

Staff Emeritus
Ok, my notation
$$|\vec{AC}|=|\vec{CE}|$$
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

#### ccseagle

C is the midpoint of lines BC and CD?

#### cristo

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?

#### ccseagle

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

#### cristo

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

#### ccseagle

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

#### cristo

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=...?

#### ccseagle

the lengths are congruent?

#### cristo

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.

#### ccseagle

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

#### cristo

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

#### ccseagle

ok, thanks..

Given: angle 8 and angle 1 are supplementary

Prove: angle 4 is congruent to angle 6

Picture:

___________________________________________

-angle 1 is congruent to angle 3 because they are vertical angles
-angle 8 is congruent to angle 6 because they are vertical angles

#### Attachments

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#### ccseagle

-supplementary means that the sum of two angles equals 180 degrees
-angle 8 and angle 1 are congruent because of corresponding angles

#### ccseagle

But now is where I get stuck

#### ccseagle

Umm, can you give me a hint please??

#### cristo

Staff Emeritus
-supplementary means that the sum of two angles equals 180 degrees
-angle 8 and angle 1 are congruent because of corresponding angles
Careful.. You said 8 and 1 were supplementary!

From what we are given, and your points in your previous post,

6=8=180-1

Now, since 1 and 2 are angles on a line, what can you say about 2 in terms of 1? how is 2 related to 4?