Perpendicular bisectors and angle bisectors

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

How do you identify a perpendicular bisector in a diagram?

Back

Look for a line that intersects a segment at its midpoint and forms right angles with that segment.

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

What is an angle bisector?

Back

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

Front

How do you identify an angle bisector in a diagram?

Back

Look for a ray that starts at the vertex of the angle and splits it into two equal angles.

Front

What is the relationship between a point on the angle bisector and the sides of the angle?

Back

Any point on the angle bisector is equidistant from the two sides of the angle.

Front

If a line segment has endpoints A(2, 3) and B(6, 7), what is the midpoint?

Back

The midpoint M is given by M = ((2+6)/2, (3+7)/2) = (4, 5).

Front

If the length of segment DC is 4, what does this imply about the segments created by its perpendicular bisector?

Back

The perpendicular bisector divides segment DC into two equal segments, each measuring 2.

Front

What is the measure of angle JKM if it is formed by two intersecting lines?

Back

If m< JKM = 38 degrees, then the angles formed by the intersecting lines can be used to find other angles using properties of vertical and adjacent angles.

Front

How can you find the length of a segment using the properties of perpendicular bisectors?

Back

Use the distance formula or the properties of congruent triangles formed by the perpendicular bisector.