Understanding Medians of a Triangle

This video tutorial covers the concept of medians in a triangle, defining them as line segments joining a vertex to the midpoint of the opposite side. It explains that each triangle has three medians, which intersect at a point called the centroid. The centroid is the center of mass for a triangle of uniform density, meaning it can balance on any line through it. The video also discusses the concurrency of medians theorem, stating that the medians intersect at a point two-thirds the distance from each vertex to the midpoint of the opposite side. Examples are provided to illustrate these properties, and the video concludes with a formal statement of the properties of medians.

What is a median in a triangle?

• A line segment joining a vertex and the midpoint of the opposite side

• A line segment joining two midpoints

• A line segment joining two vertices

• A line segment joining the centroid and a vertex

What is the centroid of a triangle?

• The midpoint of the longest side

• The intersection point of the altitudes

• The intersection point of the angle bisectors

• The intersection point of the medians

How does the centroid relate to the center of mass?

• It is the point where the triangle's perimeter is minimum

• It is the point where the triangle's area is maximum

• It is the point where the triangle's height is maximum

• It is the point where the triangle's weight is evenly distributed

According to the concurrency of medians theorem, what fraction of the median is from the vertex to the centroid?

• One-half

• One-third

• Two-thirds

• Three-fourths

If a median is 27 units long, how long is the segment from the vertex to the centroid?

• 9 units

• 18 units

• 27 units

• 13.5 units

If segment AE is 15 units, what is the length of AM?

• 15 units

• 7.5 units

• 10 units

• 5 units

What is the length of ME if AE is 15 units?

• 15 units

• 7.5 units

• 5 units

• 10 units

If BF is 12 units, what is the length of BM?

• 4 units

• 6 units

• 8 units

• 12 units

What is the relationship between ME and AM?

• ME is twice the length of AM

• ME is half the length of AM

• ME is equal to AM

• ME is one-third the length of AM

If CM is two-thirds of CD, what is the length of MD?

• Half of CD

• Twice CD

• Equal to CD

• One-third of CD