Geometry Geometry Constructions & Loci 1

Question 1

Which tools are traditionally used in geometric constructions?

Accepted Answer

Compass and straightedge

Answer

Classical geometric constructions use only a compass and a straightedge (unmarked ruler).

Question 2

What is the locus of all points equidistant from two fixed points A and B?

Accepted Answer

The perpendicular bisector of AB

Answer

The set of all points equidistant from two fixed points is the perpendicular bisector of the segment joining them.

Question 3

To bisect an angle using a compass and straightedge, what is the first step?

Accepted Answer

Place the compass point at the vertex and draw an arc intersecting both rays

Answer

The first step is to place the compass at the vertex and draw an arc that intersects both rays of the angle.

Question 4

What is the locus of all points equidistant from a fixed point (center)?

Accepted Answer

A circle

Answer

The locus of all points at a fixed distance from a center point is a circle.

Question 5

How do you construct the perpendicular bisector of a line segment?

Accepted Answer

Draw arcs from each endpoint with equal radii greater than half the segment's length, then connect the intersection points

Answer

Open the compass to more than half the segment's length, draw intersecting arcs from both endpoints, and connect the two intersection points.

Geometry Practice Test