Special Segments of Triangles

Front

What is the point of concurrency where the altitudes of a triangle intersect?

Back

The orthocenter.

Front

What is the length of segment NM if it is given as 20?

Back

NM = 20.

Front

What type of lines are the altitudes in a triangle?

Back

Altitudes are the perpendicular segments from a vertex to the opposite side.

Front

What is a median in a triangle?

Back

A median is a segment that connects a vertex to the midpoint of the opposite side.

Front

How can you find the length of segment DC using the Perpendicular Bisector Theorem?

Back

By applying the Perpendicular Bisector Theorem, which states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment.

Front

What is the definition of a triangle's centroid?

Back

The centroid is the point of concurrency of the medians of a triangle.

Front

What is the relationship between the orthocenter and the types of triangles?

Back

The orthocenter's position varies: it is inside the triangle for acute triangles, on the triangle for right triangles, and outside for obtuse triangles.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides intersect and is equidistant from the vertices of the triangle.

Front

What is the definition of an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is the relationship between the centroid and the segments it divides?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.