Medians and Altitudes

Front

What is an altitude in a triangle?

Back

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

Front

What is a median in a triangle?

Back

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

Front

What is the relationship between altitudes and angles in a triangle?

Back

Altitudes create right angles (90 degrees) with the base of the triangle.

Front

How many altitudes can be drawn in a triangle?

Back

Three altitudes can be drawn, one from each vertex.

Front

How many medians can be drawn in a triangle?

Back

Three medians can be drawn, one from each vertex to the midpoint of the opposite side.

Front

What is the point of intersection of the altitudes called?

Back

The orthocenter.

Front

What is the point of intersection of the medians called?

Back

The centroid.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the center of mass and divides each median into a ratio of 2:1.

Front

If a triangle has sides of lengths 6, 8, and 10, what is the length of the median to the longest side?

Back

The length of the median to the longest side (10) is 7.5.

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_a = 1/2 * sqrt(2b^2 + 2c^2 - a^2), where a, b, and c are the lengths of the sides.