Geometry Constructions Homework

Front

What is an angle bisector?

Back

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

Front

How do you construct an angle bisector using a compass?

Back

1. Place the compass point on the vertex of the angle. 2. Draw an arc that intersects both sides of the angle. 3. Label the intersection points. 4. Without changing the compass width, draw arcs from each intersection point. 5. Draw a line from the vertex to the intersection of the two arcs.

Front

What is a perpendicular bisector?

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 a perpendicular bisector?

Back

1. Place the compass point on one endpoint of the segment. 2. Draw an arc above and below the segment. 3. Without changing the compass width, repeat from the other endpoint. 4. Draw a line through the intersection points of the arcs.

Front

What is the definition of congruent angles?

Back

Congruent angles are angles that have the same measure.

Front

How do you construct a congruent angle?

Back

1. Draw a ray from a point. 2. Use a compass to measure the angle you want to copy. 3. Place the compass point on the endpoint of the ray and draw an arc. 4. Mark the intersection and draw a ray through it.

Front

What is the purpose of using a compass in constructions?

Back

A compass is used to create arcs and circles, which are essential for accurate geometric constructions.

Front

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

Back

An angle bisector divides an angle into two equal angles, while a segment bisector divides a line segment into two equal segments.

Front

What does it mean for segments to be congruent?

Back

Congruent segments are segments that have the same length.

Front

How do you construct congruent segments?

Back

1. Measure the length of the segment with a compass. 2. Place the compass point on a new point and draw an arc. 3. Mark the intersection point to create a segment of the same length.