What two tools are used in classical geometric constructions?
How do you bisect a line segment using a compass and straightedge?
How do you bisect an angle using a compass and straightedge?
What is a perpendicular bisector?
Which three classical construction problems were proven impossible with compass and straightedge alone?
Hint: All proven impossible in the 19th century
What is the circumcenter of a triangle?
What is the incenter of a triangle?
How do you construct a perpendicular line to a given line through a point not on that line?
How do you copy a given angle using only a compass and straightedge?
Hint: The compass preserves distances, so it can transfer the arc's 'width' to a new location
How do you construct an equilateral triangle on a given segment using compass and straightedge?
Hint: This is Euclid's very first proposition in the Elements
Which regular polygons did the ancient Greeks prove could be constructed with only a compass and straightedge?
Hint: A regular heptagon (7 sides) is famously NOT among them
Why is 'doubling the cube' impossible with only a compass and straightedge?
Hint: Compass-and-straightedge constructions can only produce certain kinds of numbers