Geometric Constructions

Front

What is the definition of an angle bisector?

Back

An angle bisector is a line or ray that divides an angle into two equal parts.

Front

What does the term 'perpendicular bisector' refer to?

Back

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

Front

How do you construct an angle bisector using a compass and straightedge?

Back

1. Place the compass point on the vertex of the angle. 2. Draw an arc that intersects both rays of the angle. 3. Without changing the compass width, place the compass point on each intersection point and draw arcs that intersect. 4. Draw a line from the vertex to the intersection of the arcs.

Front

What is the significance of the term 'bisection' in geometry?

Back

Bisection in geometry refers to the process of dividing a geometric figure into two equal parts.

Front

What is the first step in constructing a perpendicular bisector of a segment?

Back

The first step is to place the compass point on one endpoint of the segment and draw an arc above and below the segment.

Front

What is the relationship between an angle bisector and the angles it creates?

Back

The angle bisector creates two angles that are congruent to each other.

Front

What tools are commonly used for geometric constructions?

Back

The common tools used for geometric constructions are a compass and a straightedge.

Front

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

Back

A compass is used to draw arcs and circles, which are essential for creating precise geometric figures.

Front

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

Back

To verify, measure the segments on either side of the line; if they are equal and the angles formed are right angles, it is a perpendicular bisector.

Front

What is the difference between a segment bisector and a perpendicular bisector?

Back

A segment bisector divides a segment into two equal parts, while a perpendicular bisector does so at a right angle.