Perpendicular Bisector

Front

What is a perpendicular bisector?

Back

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

Front

How can you identify a perpendicular bisector in a triangle?

Back

It is the line segment that is perpendicular to one side of the triangle and passes through the midpoint of that side.

Front

What is the relationship between a perpendicular bisector and the points on the line segment it bisects?

Back

Any point on the perpendicular bisector is equidistant from the endpoints of the line segment.

Front

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

Back

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

Front

If line segment AB is bisected by line segment CD at point E, what can be said about AE and EB?

Back

AE is equal to EB.

Front

In a right triangle, what is the relationship between the altitude from the right angle and the hypotenuse?

Back

The altitude from the right angle to the hypotenuse is the geometric mean of the two segments it creates on the hypotenuse.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of the triangle intersect, and it is equidistant from all three vertices.

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 line. 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 equation of a perpendicular bisector in a coordinate plane?

Back

If the endpoints of a segment are (x1, y1) and (x2, y2), the slope of the perpendicular bisector is -1/m, where m is the slope of the segment.

Front

What is the relationship between the slopes of two perpendicular lines?

Back

The product of their slopes is -1.