Medians and Centroids in Triangles

The video tutorial explains the concept of the centroid in a triangle, where the medians intersect. It highlights the property that the centroid divides each median into two segments, with the longer segment being twice the length of the shorter one. The tutorial then applies this property to solve problems involving the centroid, demonstrating how to calculate the lengths of segments in a triangle using given measurements.

What is the centroid of a triangle?

• The point where the angle bisectors intersect

• The point where the medians intersect

• The point where the altitudes intersect

• The point where the perpendicular bisectors intersect

What is a median in a triangle?

• A line from a vertex to the opposite side's altitude

• A line from a vertex to the opposite side's angle bisector

• A line from a vertex to the opposite side's vertex

• A line from a vertex to the opposite side's midpoint

How does the centroid divide each median?

• Into two equal parts

• Into three equal parts

• Into a 2:1 ratio

• Into a 3:1 ratio

What is the length of the longer segment of a median if the whole median is 21 units?

• 21 units

• 10.5 units

• 14 units

• 7 units

In the given problem, what is the length of segment VU?

• 10 units

• 14 units

• 21 units

• 7 units

If VU is 10 units, what is the length of the longer segment of the median?

• 30 units

• 20 units

• 15 units

• 10 units

What is the total length of the median if the shorter segment is 7 units?

• 35 units

• 28 units

• 21 units

• 14 units

What is the length of segment RS if the shorter segment is 7 units?

• 28 units

• 21 units

• 14 units

• 7 units

What is the relationship between the lengths of the segments divided by the centroid?

• The longer segment is twice the shorter segment

• The longer segment is three times the shorter segment

• The longer segment is half the shorter segment

• The longer segment is equal to the shorter segment

If the whole median is 21 units, what is the length of the shorter segment?

• 14 units

• 7 units

• 21 units

• 10 units