Geometry Constructions & Loci Flashcards
6 cards from real Geometry practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 Geometry Constructions & Loci flashcards as text
What is the locus of all points equidistant from two intersecting lines?
Answer: The two angle bisectors of the angles formed
The locus of points equidistant from two intersecting lines consists of the two angle bisectors of the angles they form.
Which is NOT a valid classical geometric construction?
Answer: Trisecting an arbitrary angle with compass and straightedge only
Trisecting an arbitrary angle using only compass and straightedge is impossible, as proven by Pierre Wantzel in 1837.
To copy a given angle at a new vertex, you first:
Answer: Draw a ray from the new vertex, then recreate the arc and chord lengths of the original angle
Draw a ray from the new vertex, use the same compass radius to draw an arc, then measure and transfer the chord length to recreate the angle.
What is a locus in geometry?
Answer: The set of all points that satisfy a given condition or rule
A locus is the complete set of all points (and only those points) that satisfy a stated geometric condition.
Constructing the incenter of a triangle requires:
Answer: Bisecting all three angles and finding their intersection
The incenter is found by bisecting all three interior angles; their intersection is equidistant from all three sides.
To construct a regular hexagon inscribed in a circle, you:
Answer: Set the compass to the circle's radius and step off six equal arcs around the circle
The radius of a circle equals the side length of the inscribed regular hexagon, so stepping the compass radius around the circle marks six equally spaced points.