Note Taking-Module 3:Medians Altitudes Bisectors and Midsegments

Circumference

• The circumference is the distance around a circle.

• The circumference is the intersection point of three perpendicular bisectors of the sides of a triangle.

• The circumference is the area enclosed by a triangle.

• The circumference is the longest side of a triangle.

Centroid

• The centroid of a triangle is the intersection point of its three medians.

• The centroid is the point where the altitudes of a triangle intersect.

• The centroid is the midpoint of the longest side of a triangle.

• The centroid is the point equidistant from all three vertices of a triangle.

Median

• A median is a segment with endpoints at a vertex of the triangle and the midpoint of the opposite side.

• A median is a line segment that connects two vertices of a triangle.

• A median is a line that bisects an angle of a triangle.

• A median is a segment that divides a triangle into two equal areas.

What is the importance of understanding bisectors in geometry?

• Bisectors are only used in advanced mathematics.

• Bisectors help in constructing angles and segments, and are essential in proofs and constructions in geometry.

• Bisectors are irrelevant in practical applications.

• Bisectors are primarily used in algebra.

Orthocenter

• The point where the three medians of a triangle intersect.

• The point where the three altitudes of a triangle intersect.

• The center of the circumcircle of a triangle.

• The point where the three angle bisectors of a triangle intersect.

Take Notes on these Vocabulary

• Median

• Circumference

• Radius

• Diameter

Perpendicular Bisector

• A line that is parallel to a side of a triangle.

• A line that passes through the midpoint of a side and is perpendicular to that side.

• A line that connects two opposite vertices of a polygon.

• A line that bisects an angle of a triangle.

Angle Bisector

• A line that connects two points on a circle.

• A ray that divides an angle into two equal angles.

• A segment that forms a right angle with another segment.

• A line that extends infinitely in both directions.

Midsegment

• A segment that connects the midpoints of two sides of a triangle.

• A segment that bisects an angle of a triangle.

• A segment that connects the centroid to a vertex of a triangle.

• A segment that is perpendicular to one side of a triangle.

Incenter

• The incenter of a triangle is the intersection point of the three angle bisectors and the center of the incircle, which is the largest circle that can fit inside the triangle.

• The incenter is the point where the three medians of a triangle intersect.

• The incenter is the point where the three altitudes of a triangle intersect.

• The incenter is the center of the circumcircle of a triangle.