Chapter 5.2

Question 1

Angle bisector of a triangle

Answer 1

A segment that bisects one of the angles of the triangle

Question 2

Median

Answer 2

A segment whose endpoints are a vertex and the midpoint of the opposite side

Question 3

Altitude

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 segment that intersect in a single point

Question 5

Circumcenter

Answer 5

Equidistant from the vertices of the triangle

Question 6

Incenter

Answer 6

Equidistant from the three sides of the triangle

Question 7

Centroid

Answer 7

Two thirds of the distance from each vertex to the midpoint of the opposite side

Question 8

Orthocenter

Answer 8

Common point of lines containing altitudes of triangles

Question 9

Theorem 5.5 – concurrency properties

Answer 9

The lines containing the perpendicular bisectors of a triangle are concurrent. Their common point is the circumcenter of the triangle. The circumcenter is equidistant from the vertices of the triangle. The angle bisectors of a triangle are concurrent. There common point is the incenter of the triangle. The incenter is equidistant from the three sides of the triangle. 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. The lines containing the altitudes of a triangle are concurrent. Their common point is the orthocenter of the triangle.

Question 10

Perpendicular bisector of a triangle

Answer 10

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