Constructions

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

Define angle bisector.

Back

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

Front

What is the construction for finding the midpoint of a line segment?

Back

To find the midpoint, draw two circles with the same radius from each endpoint of the segment. The intersection points of the circles determine the midpoint.

Front

How do you construct a perpendicular line to a point on a line?

Back

To construct a perpendicular line to a point on a line, use a compass to draw a circle centered at the point, then draw two arcs that intersect the line. Connect the intersection points to the center.

Front

What is the purpose of copying an angle?

Back

Copying an angle allows you to create an angle that is congruent to a given angle using a compass and straightedge.

Front

What is the construction for drawing a parallel line to a point not on the line?

Back

To draw a parallel line to a point not on the line, use a compass to create a transversal that intersects both the line and the point, then replicate the angle formed at the intersection.

Front

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

Back

An altitude is a line segment from a vertex of a triangle perpendicular to the opposite side, while a perpendicular bisector divides a segment into two equal parts at a right angle.

Front

What are corresponding angles?

Back

Corresponding angles are pairs of angles that are in similar positions at each intersection where a straight line crosses two others.

Front

Explain the concept of vertical angles.

Back

Vertical angles are the angles opposite each other when two lines intersect. They are always equal.

Front

What is the significance of constructing an angle bisector in geometry?

Back

Constructing an angle bisector is significant for creating equal angles, which is essential in various geometric proofs and constructions.