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

A circle at their intersection

Answer

A line parallel to each

Answer

The perpendicular bisector of the segment between them

Question 2

Which is NOT a valid classical geometric construction?

Accepted Answer

Trisecting an arbitrary angle with compass and straightedge only

Answer

Bisecting a line segment

Answer

Constructing a 60° angle

Answer

Copying a given angle

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

Measure the angle in degrees and mark it at the new vertex

Answer

Draw a circle at the original vertex the same size as the new one

Answer

Construct the perpendicular bisector of the original 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 single fixed point that satisfies a condition

Answer

The midpoint of a line segment

Answer

A specific type of angle bisector

Question 5

Constructing the incenter of a triangle requires:

Accepted Answer

Bisecting all three angles and finding their intersection

Answer

Bisecting all three sides and finding their intersection

Answer

Drawing altitudes from all three vertices

Answer

Finding the midpoints of all three sides

Question 6

To construct a regular hexagon inscribed in a circle, you:

Accepted Answer

Set the compass to the circle's radius and step off six equal arcs around the circle

Answer

Divide the circle into six equal 60° angles using a protractor

Answer

Draw three diameters at equal 60° angles and connect the endpoints

Answer

Bisect the circle's diameter three times