Perpendicular Bisectors and Angle Bisectors

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

What is an angle bisector?

Back

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

Front

If segment AB is 20 units long, what is the length of each segment created by its perpendicular bisector?

Back

10 units each.

Front

What is the relationship between the angles formed by a perpendicular bisector and the original segment?

Back

The angles formed are right angles (90 degrees).

Front

If angle ABC is 50 degrees, what is the measure of angle ABD if BD is the angle bisector?

Back

25 degrees.

Front

How do you find the length of a segment when given the coordinates of its endpoints?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the significance of the point where the perpendicular bisectors of a triangle intersect?

Back

It is called the circumcenter, which is equidistant from all vertices of the triangle.

Front

If angle DBC is 30 degrees, what is the measure of angle DBA if B is the angle bisector?

Back

30 degrees.

Front

What is the formula for finding the midpoint of a segment with endpoints (x1, y1) and (x2, y2)?

Back

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2).

Front

In a triangle, if one angle measures 60 degrees, what can you say about the other two angles?

Back

They must sum to 120 degrees.