11.3 Vertically opposite
When 2 straight lines cross each other, 4 angles are formed. We will call these a, b, c, d as per this diagram:
Vertically opposite angles are equal to each other. In other words, angles a=c, and b=d.
Why? We know angles on a straight line add up to 180°. That means . We also know that . We can reshuffle the first formula such that , and the second formula to . Therefore, we know that . Simplifying, , meaning . Quod erat demonstrandum.
“Hey, what do those weird Greek letters mean?” Mandy asked.
“It’s telling other mathematicians you’ve set out what you intended to prove,” Jamie responded, “essentially a sign of relief!”
Angles such as a and c, or b and d are called vertically opposite, because they are opposite the vertex where the 2 lines meet.
Vertically opposite angles are equal to each other.