AI Tutor
If a surveyor measures just one angle at a busy five-way street intersection, can they figure out every single other angle without measuring again?
Yes! Geometric rules work like falling dominoes — knowing one angle triggers a deductive chain, where each fact you discover unlocks the next unknown.
To build these chains, what core angle tools do we need in our detective toolkit?

The Core Angle Tools

When two straight lines cross, they form a linear pair — two side-by-side angles on a straight line that always add up to 180∘180^\circ.
They also form vertical angles, which are opposite angles across the intersection point that are always equal to each other.
Around 600 BCE, the Greek philosopher Thales of Miletus proved that vertical angles are always equal by showing both angles share the exact same supplementary neighbor.
What happens when three lines intersect at the very same point to create a web of six angles?

Building a Deductive Chain

In complex diagrams, you cannot solve everything in one giant leap.
Instead, you write a step-by-step justification: state a rule, calculate an angle, and use that new number to crack the next piece.