Geometry Geometry Constructions & Loci 3

Question 1

What is the locus of all points equidistant from two intersecting lines?

Accepted Answer

The two angle bisectors of the angles formed

Answer

The locus of points equidistant from two intersecting lines consists of the two angle bisectors of the angles they form.

Question 2

Which is NOT a valid classical geometric construction?

Accepted Answer

Trisecting an arbitrary angle with compass and straightedge only

Answer

Trisecting an arbitrary angle using only compass and straightedge is impossible, as proven by Pierre Wantzel in 1837.

Question 3

To copy a given angle at a new vertex, you first:

Accepted Answer

Draw a ray from the new vertex, then recreate the arc and chord lengths of the original angle

Answer

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.

Question 4

What is a locus in geometry?

Accepted Answer

The set of all points that satisfy a given condition or rule

Answer

A locus is the complete set of all points (and only those points) that satisfy a stated geometric condition.

Question 5

Constructing the incenter of a triangle requires:

Accepted Answer

Bisecting all three angles and finding their intersection

Answer

The incenter is found by bisecting all three interior angles; their intersection is equidistant from all three sides.

Geometry Practice Test