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 the formula for finding 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 side opposite the median.

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 a perpendicular line from a vertex to the opposite side.

Front

In triangle ABC, if D is the midpoint of BC, what is AD?

Back

AD is the median of triangle ABC.

Front

If a triangle has sides of lengths 3, 4, and 5, what is the length of the median to the side of length 5?

Back

The length of the median to the side of length 5 is 4.

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.