MHB What is the proof for angle equality?

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When two lines intersect, they create opposite angles that are equal due to the properties of vertical angles. This relationship is grounded in the theorem stating that angles formed by intersecting lines are equal when their sides are perpendicular. The proof of angle equality can be derived from this theorem, demonstrating both the "how" and "why" of their equality. Understanding this fundamental concept is essential in geometry. The discussion highlights the importance of recognizing the properties of intersecting lines in proving angle relationships.
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I've been searching over the internet and geometry books for the proof of the relationship of these two angles but I couldn't find one. Can you tell me the "how" and "why" of their equality. thanks and regards!
 

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Use the fact that when two lines intersect, opposite angles are equal. The result then follows.
 
Check post #5.

http://mathhelpboards.com/trigonometry-12/equality-angles-11593.html

"There is a theorem saying that two angles whose sides are mutually perpendicular are equal. "
 
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