Medians and Midsegments flashcard

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

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 relationship between AG and GD?

Back

AG is twice the length of GD. If AG = 16, then GD = 8.

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 a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle.

Front

How does the length of a midsegment compare to the lengths of the sides of the triangle?

Back

The length of a midsegment is half the length of the side it is parallel to.

Front

What is the point of concurrency for the medians of a triangle called?

Back

The point of concurrency for the medians of a triangle is called the centroid.

Front

If a triangle has a median of length 11.5, what can be inferred about the triangle?

Back

The median divides the triangle into two smaller triangles of equal area.

Front

What is the significance of the centroid in a triangle?

Back

The centroid divides each median into a ratio of 2:1, with the longer segment being closer to the vertex.

Front

In triangle ABC, if AG = 16, what is the length of the entire median from A to the midpoint of BC?

Back

The entire median length is AG + GD = 16 + 8 = 24.