Geometry Basics Mastery Hub: The Industry Foundation Practic

In Euclidean geometry, which of the following is a fundamental axiom regarding the existence of a unique line?

tests understanding of Euclid's postulates, specifically the one that states "A straight line can be drawn joining any two points." This is a foundational concept for constructing geometric figures and proving theorems. Option A is incorrect because infinitely many circles can pass through two points. Option B is incorrect because infinitely many planes can contain two distinct points (they define a line, and a plane can rotate around that line). Option D is incorrect; three non-collinear points define a unique plane, not a unique line (they would define two lines if considered pairwise). Question: Consider a triangle ABC with angles $\angle A = 30^\circ$ and $\angle B = 60^\circ$. According to Euclidean geometry's angle sum property, what is the measure of $\angle C$?

In a Euclidean plane, two distinct lines are either parallel or intersect at exactly one point. If line L1 is parallel to line L2, and line L2 is parallel to line L3, what can be definitively concluded about the relationship between line L1 and line L3?