Medians of Triangles

Front

What is a median in a triangle?

Back

A median of a triangle is a line segment that connects a vertex to the midpoint 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 center of mass of the triangle.

Front

If G is the centroid of triangle ABC, what is the ratio of the lengths of the segments created by the median?

Back

The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice the length of the segment connecting the centroid to the midpoint of the opposite side.

Front

How do you find the length of a segment when given the length of the median?

Back

If the length of the median is known, the length of the segment from the vertex to the centroid is 2/3 of the median's length, and the length from the centroid to the midpoint is 1/3.

Front

What is the relationship between the lengths of the segments created by a median?

Back

If a median divides a triangle into two smaller triangles, the areas of these triangles are equal.

Front

If BE is a median in triangle ABC and BE = 18, what is the length of BG?

Back

BG = 6, since G is the centroid and divides BE in a 2:1 ratio.

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 side opposite the median.

Front

If CF is a median and BF = 10, what is the length of AF?

Back

AF = 10, since the median divides the opposite side into two equal segments.

Front

What is the significance of the midpoint in relation to a median?

Back

The midpoint is the point on the side of the triangle that the median connects to the opposite vertex.

Front

What are the four special segments of a triangle?

Back

The four special segments are the altitude, median, angle bisector, and midsegment.