Perpendicular and Angle Bisectors

Front

What is a perpendicular bisector?

Back

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

Front

Define angle bisector.

Back

A ray that divides an angle into two equal angles.

Tags

CCSS.HSG.CO.C.9

Front

What is the relationship between perpendicular bisectors and triangles?

Back

The perpendicular bisectors of a triangle intersect at a point called the circumcenter, which is equidistant from the vertices.

Tags

CCSS.HSG.C.A.3

Front

What is the significance of the circumcenter in a triangle?

Back

It is the center of the circumcircle, the circle that passes through all three vertices of the triangle.

Tags

CCSS.HSG.C.A.3

Front

How do you construct a perpendicular bisector of a segment?

Back

1. Place the compass point on one endpoint and draw an arc above and below the segment. 2. Repeat from the other endpoint. 3. Draw a line through the intersection points of the arcs.

Tags

CCSS.HSG.CO.C.9

Front

What is the difference between a median and a perpendicular bisector?

Back

A median connects a vertex to the midpoint of the opposite side, while a perpendicular bisector divides a segment into two equal parts at a right angle.

Tags

CCSS.HSG.CO.C.10

Front

What is the measure of angles formed by an angle bisector?

Back

The angle bisector divides the angle into two equal parts, so each part measures half of the original angle.

Front

If two angles are congruent, what can be said about their angle bisectors?

Back

The angle bisectors of congruent angles are also congruent.

Tags

CCSS.HSG.CO.C.9

Front

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

Back

The angles formed are right angles (90 degrees) to the segment.

Tags

CCSS.HSG.CO.C.9

Front

How can you verify that a point lies on the perpendicular bisector of a segment?

Back

If the distances from the point to the endpoints of the segment are equal, then the point lies on the perpendicular bisector.

Tags

CCSS.HSG.CO.C.9