5.2 Medians & Altitudes*

Front

What is a median in a triangle?

Back

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

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is an altitude in a triangle?

Back

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

Front

How many altitudes does a triangle have?

Back

A triangle has three altitudes, one from each vertex.

Front

What is the difference between a median and an altitude?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude is perpendicular to the opposite side.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a right angle.

Front

How do you find the length of a median in a triangle?

Back

The length of a median can be found using the formula: m = 1/2 * √(2a² + 2b² - c²), where a and b are the lengths of the sides adjacent to the median, and c is the length of the opposite side.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it is also the triangle's center of mass.

Front

What is the relationship between the centroid and the medians?

Back

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

Front

In triangle GHI, if HK is an altitude, what does that imply about angle HKI?

Back

Angle HKI is a right angle (90 degrees) because an altitude is perpendicular to the opposite side.