5.2 Special Segments in a Triangle

Question 1

Angle Bisector of a Triangle

Answer 1

A segment that bisects one of the angles of a triangle.

Question 2

Median of a Triangle

Answer 2

A segment who’s endpoints are a vertex of the triangle and the midpoint of the opposite side

Question 3

Altitude of a Triangle

Answer 3

A segment from a vertex that is perpendicular to the opposite side or to the line containing the opposite side.

Question 4

Concurrent

Answer 4

Two or more lines or segments are concurrent if they intersect in a single point

Question 5

Circumcenter

Answer 5

The lines containing the perpendicular bisectors of the sides of a triangle are concurrent. Their common point is the circumcenter of the triangle. The circumcenter is equidistant from the 3 vertices of the triangle and is the center of the circumscribed circle

Question 6

Incenter

Answer 6

The angle bisectors of a triangle are concurrent in the incenter of the triangle. The incenter is equidistant from the 3 sides of the triangle and is the center of the inscribed circle.

Question 7

Centroid

Answer 7

The medians of a triangle are concurrent. Their common point is the centroid of the triangle. The centroid is two-thirds of the distance from each vertex to the midpoint of the opposite side

Question 8

Orthocenter

Answer 8

The lines containing the altitudes of a triangle are concurrent in the orthocenter of the triangle

Question 9

Perpendicular Bisector of a Triangle

Answer 9

A segment that is part of a perpendicular bisector of one of the sides