Constructions Geometry

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a line segment into two equal parts at a 90-degree angle.

Front

How do you construct a perpendicular bisector using a compass and straightedge?

Back

1. Place the compass point on one endpoint of the segment and draw an arc above and below the segment. 2. Without changing the compass width, repeat from the other endpoint. 3. Draw a line through the intersection points of the arcs.

Front

What is the purpose of using a compass in geometric constructions?

Back

A compass is used to draw arcs and circles, measure distances, and transfer lengths accurately.

Front

What is the first step in copying a line segment using a compass?

Back

The first step is to measure the length of the original line segment with the compass.

Front

What does it mean to bisect an angle?

Back

To bisect an angle means to divide it into two equal angles.

Front

What is the difference between a perpendicular bisector and an angle bisector?

Back

A perpendicular bisector divides a line segment into two equal parts at a right angle, while an angle bisector divides an angle into two equal angles.

Front

What is the significance of the midpoint in constructions?

Back

The midpoint is the point that divides a segment into two equal lengths, essential for constructing perpendicular bisectors.

Front

How can you verify that a line is a perpendicular bisector?

Back

You can verify it by checking that it intersects the segment at its midpoint and forms right angles with the segment.

Front

What is the role of arcs in geometric constructions?

Back

Arcs help locate points of intersection and are used to create angles and bisectors.

Front

What is an altitude in geometry?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.