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The response includes the vertical angles theorem, the corresponding angles theorem, and the transitive property. Supplementary angles and linear pairs are not mentioned.
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Vertical angles, formed when two lines intersect, are always congruent. This delightful little theorem has roots in ancient geometry, confirmed by the likes of Euclid, who made sure we understood their power! Imagine two foes in battle, staring across at each other—these angles are reflections of one another, always equal.
When we dive into real-world applications, think of engineering and architecture, where precise angles are crucial. Architects must ensure their design angles adhere to these principles for stability and aesthetic appeal. So next time you look at a building, remember: those angles are working hard to keep everything standing tall and proud!

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