Geometry Proof - Parallel Lines

1. Sep 25, 2012

Buzur

1. The problem statement, all variables and given/known data
Given: AB $\coprod$ CD ; $\angle$A $\cong$ $\angle$C
Proof: AD $\coprod$ BC

2. Relevant equations

Idk how to necessary finish it...

3. The attempt at a solution

Statement -------------- Proof
1. AB $\coprod$ CD ; $\angle$A $\cong$ $\angle$C ----------- 1. Given
2. I say $\angle$A is supp. $\angle$D and $\angle$B is supp. $\angle$C ----------- 2. If two parallel lines cut by a transversal, then same-side interior angles are supp.

3. AD $\coprod$ BC ---------------- 3. Substitution Prop.
1. The problem statement, all variables and given/known data

2. Sep 25, 2012

marty1

I don't think you can prove that TRUE unless ∠ A = ∠ C exactly.

3. Sep 25, 2012

Buzur

they are equal.. it was in the given information!

4. Sep 26, 2012

HallsofIvy

Staff Emeritus
What are you substuting into what? Are you saying you are substituting "AD"
for "AB" and "BC" for "CD" in the original statement? That's NOT what the "substitution prop." says! Nor can you simply substitute them into the theorem you stated about parallel lines and supplementary angles- you would need to use its converse which says that if a transversal cutting two lines forms supplementary angles then the lines are parallel.

5. Sep 26, 2012