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 relationship between the medians of a triangle and its centroid?

Back

The centroid is the point where all three medians intersect, and it divides each median into a ratio of 2:1.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

How is a perpendicular bisector different from a median?

Back

A perpendicular bisector intersects a segment at its midpoint and is perpendicular to it, while a median connects a vertex to the midpoint of the opposite side.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the center of mass of the triangle and is the point of balance.

Front

What is the formula to find the length of a median in a triangle?

Back

The length of a median can be calculated 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 difference between an altitude and an angle bisector?

Back

An altitude is a perpendicular segment from a vertex to the opposite side, while an angle bisector divides an angle into two equal angles.