Midsegment and Medians

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. It is parallel to the third side and its length is half the length of that side.

Front

What is the relationship between a midsegment and the sides of a triangle?

Back

The midsegment is parallel to one side of the triangle and its length is half the length of that side.

Front

How do you find the length of a midsegment?

Back

To find the length of a midsegment, measure the lengths of the two sides it connects, find their midpoints, and then use the formula: Length of midsegment = 1/2 * Length of the third side.

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 point of intersection of the medians called?

Back

The point of intersection of the medians is called the centroid.

Front

What is the centroid of a triangle?

Back

The centroid is the point where all three medians intersect, and it is also the center of mass of the triangle.

Front

What is the relationship between the centroid and the medians?

Back

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

Front

How do you calculate the length of a median?

Back

To calculate the length of a median, use the formula: Median = √(2a² + 2b² - c²) / 4, 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

What is the significance of the centroid in a triangle?

Back

The centroid is significant because it is the balance point of the triangle, meaning if the triangle were made of a uniform material, it would balance perfectly at the centroid.