Special Segments in Triangles

Front

What is an Angle Bisector?

Back

An angle bisector is a segment that divides an angle into two equal parts.

Front

What is a Median in a triangle?

Back

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

Front

What is an Altitude in a triangle?

Back

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

Front

What is a Perpendicular Bisector?

Back

A perpendicular bisector is a segment that is perpendicular to a side of a triangle at its midpoint.

Front

What is the centroid of a triangle?

Back

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

Front

How does the centroid divide each median?

Back

The centroid divides each median into two segments, with the shorter segment being one third the length of the entire median.

Front

If AG = 10 in triangle ABC, what is AE?

Back

AE = 15, since the centroid divides the median in a 2:1 ratio.

Front

What is the relationship between the lengths of segments created by the centroid?

Back

The centroid divides each median into a ratio of 2:1, with the longer segment being twice the length of the shorter segment.

Front

What is the definition of a triangle's altitude?

Back

An altitude is a line segment from a vertex to the opposite side, forming a right angle with that side.

Front

What is the significance of the perpendicular bisector in a triangle?

Back

The perpendicular bisector of a side of a triangle is the locus of points equidistant from the endpoints of that side.