5.1 Angle/Perpendicular Bisectors

Front

What is an angle bisector?

Back

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

Front

What does a perpendicular bisector do?

Back

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

Front

If angle A measures 80 degrees, what is the measure of each angle formed by the angle bisector?

Back

40 degrees.

Front

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

Back

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

Front

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

Back

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

Front

What is the definition of a median in a triangle?

Back

A median is a line segment from a vertex to the midpoint of the opposite side.

Front

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

Back

An angle bisector divides an angle into two equal parts, while a median connects a vertex to the midpoint of the opposite side.

Front

If a triangle has angles measuring 30, 60, and 90 degrees, what is the measure of the angle bisector of the 60-degree angle?

Back

The angle bisector will measure 30 degrees for each of the two angles formed.

Front

What is the significance of the circumcenter in relation to perpendicular bisectors?

Back

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

Front

How can you determine if a line is a perpendicular bisector?

Back

A line is a perpendicular bisector if it intersects a segment at its midpoint and forms right angles with the segment.