Triangles and parallel lines problem

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Homework Help Overview

The discussion revolves around a geometry problem involving triangles and parallel lines, specifically focusing on angle relationships and congruencies to establish parallelism between two lines.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the congruence of angles and the implications for proving parallel lines. There are attempts to express angles in terms of others, and questions arise regarding the relationships between these angles.

Discussion Status

Some participants have provided guidance on angle relationships and congruences, while others are exploring how to express certain angles in terms of others. There is an ongoing exploration of the relationships without a clear consensus on the next steps.

Contextual Notes

Participants are navigating through the constraints of the problem, including the need to demonstrate specific angle congruences to prove parallel lines, and there are indications of confusion regarding angle relationships.

lingping7
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The picture has the problem and my attempts, I need guidance.
Thanks in advance
 

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Okay, you are given that angle 1 is congruent to angle 4 and angle 2 is congruent to angle 3 (you should say that in the proof). Angle 1 is congruent to angle 2 by "VOA" (vertical angles) so all of angles 1, 2, 3, and 4 are congruent to one another. To prove that AC is parallel to BD, you need to show that angle 4 is congruent to angle 6 or that angle 5 is congruent to angle 3 (alternate interior angles).
 
Yes that is true, I'm able to get angle 5 = to angle 6, but can't equate either of these angles to angle 1,2,3,4
 
How can you express the measure of angle 3? Can you express the measure of angle 5 in the same way?
[edit] I think I was transposing the 4 and the 6. >_<
 
Last edited:
Angle 3 = 180-angle6-angle2
Angle 5 = 180-angle4-angle1
I could say Angle 5 = 180-angle2-angle2
I still don't get it :(
 

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