Geometry Proof - Parallel Lines

  • Thread starter Buzur
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  • #1
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Homework Statement


Given: AB [itex]\coprod[/itex] CD ; [itex]\angle[/itex]A [itex]\cong[/itex] [itex]\angle[/itex]C
Proof: AD [itex]\coprod[/itex] BC


Geo Proof.png



Homework Equations



Idk how to necessary finish it...


The Attempt at a Solution



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

3. AD [itex]\coprod[/itex] BC ---------------- 3. Substitution Prop.

Homework Statement

 

Answers and Replies

  • #2
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I don't think you can prove that TRUE unless ∠ A = ∠ C exactly.
 
  • #3
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they are equal.. it was in the given information!
 
  • #4
HallsofIvy
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Homework Statement


Given: AB [itex]\coprod[/itex] CD ; [itex]\angle[/itex]A [itex]\cong[/itex] [itex]\angle[/itex]C
Proof: AD [itex]\coprod[/itex] BC


View attachment 51205


Homework Equations



Idk how to necessary finish it...


The Attempt at a Solution



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

3. AD [itex]\coprod[/itex] 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.
 
  • #5
81
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they are equal.. it was in the given information!

check your symbol... ≅
 
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