Flashcard 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

A ray that divides an angle into two congruent angles.

Front

How do you find the midpoint of a segment?

Back

The midpoint is found by averaging the x-coordinates and the y-coordinates of the endpoints of the segment.

Front

If AB = 10, what is the length of each segment created by the perpendicular bisector?

Back

Each segment is 5 units long.

Front

What is the relationship between a perpendicular bisector and the endpoints of a segment?

Back

The perpendicular bisector is equidistant from the endpoints of the segment.

Front

If a point lies on the perpendicular bisector of a segment, what can be said about its distance to the endpoints?

Back

It is equidistant from both endpoints.

Front

What is the formula for finding the length of a segment given its endpoints (x1, y1) and (x2, y2)?

Back

Length = √((x2 - x1)² + (y2 - y1)²).

Front

In triangle ABC, if D is the midpoint of BC, what can be said about AD if it is a perpendicular bisector?

Back

AD is perpendicular to BC and bisects it at point D.

Front

What is the significance of the angle bisector theorem?

Back

It states that the angle bisector divides the opposite side into segments that are proportional to the adjacent sides.

Front

If the measure of angle A is 40 degrees, what are the measures of the two angles formed by the angle bisector?

Back

Each angle measures 20 degrees.