Medians and Midsegments flashcard

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

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 and AG = 16, what is the length of GD?

Back

8

Front

How many medians does a triangle have?

Back

A triangle has three medians.

Front

If a triangle has one median, what is the minimum number of sides it can have?

Back

A triangle must have at least three sides.

Front

If LN = 5, what is the length of AC if AC is twice the length of LN?

Back

10

Front

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

Back

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

Front

If a triangle has two medians, what can be inferred about its sides?

Back

The triangle must have at least three sides, and the medians can provide information about the lengths of the sides.

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 * sqrt(2a^2 + 2b^2 - c^2), 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 a triangle has two medians measuring 6.6 and 13.2, what is the total length of the medians?

Back

19.8