5.2 Medians & Altitudes*

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of the 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 the centroid of a triangle?

Back

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

Front

If a median divides a triangle into two equal areas, what does this imply?

Back

It implies that the median bisects the triangle into two triangles of equal area.

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 do you find the length of a median using the formula?

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 relationship between the medians and the sides of a triangle?

Back

The medians of a triangle are related to the sides in that they can be used to find the area of the triangle.

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

If CF, BE, and AD are the medians of a triangle, what can be said about their lengths?

Back

The lengths of the medians can be calculated using the lengths of the sides of the triangle.

Front

What is the formula for finding the area of a triangle using its medians?

Back

Area = (4/3) * √(s(s - m1)(s - m2)(s - m3)), where s is the semi-perimeter and m1, m2, m3 are the lengths of the medians.