Geometry Proof - Parallel Lines

Buzur

Homework Statement

Given: AB $\coprod$ CD ; $\angle$A $\cong$ $\angle$C
Proof: AD $\coprod$ BC

Homework Equations

Idk how to necessary finish it...

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.

Homework Statement

marty1
I don't think you can prove that TRUE unless ∠ A = ∠ C exactly.

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

Homework Helper

Homework Statement

Given: AB $\coprod$ CD ; $\angle$A $\cong$ $\angle$C
Proof: AD $\coprod$ BC

View attachment 51205

Homework Equations

Idk how to necessary finish it...

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.

Homework Statement

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.

marty1
they are equal.. it was in the given information!