Understanding Medians and Centroids

This video tutorial explains how to use the properties of medians in triangles to determine unknown segment lengths. It begins with a review of the concurrency of medians theorem, which states that medians intersect at the centroid, a point two-thirds the distance from each vertex to the midpoint of the opposite side. The tutorial provides examples of calculating segment lengths using given median lengths and algebraic expressions. It emphasizes the relationship between the shorter and longer segments of a median, where the shorter segment is half the length of the longer segment. The video concludes with solving problems involving variables to find segment lengths.

What is the point called where the medians of a triangle intersect?

• Circumcenter

• Incenter

• Centroid

• Orthocenter

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

• 20 units

• 15 units

• 10 units

• 5 units

If the shorter segment of a median is half the length of the longer segment, what is the ratio of the shorter segment to the entire median?

• 1:5

• 1:3

• 1:4

• 1:2

Given BG is 5 units, what is the length of BE?

• 5 units

• 20 units

• 10 units

• 15 units

If CG is 16 units, what is the length of GF?

• 32 units

• 24 units

• 8 units

• 16 units

If AD is 30 units, what is the length of AG?

• 10 units

• 25 units

• 15 units

• 20 units

In a triangle, if the longer segment of a median is 20 units, what is the length of the entire median?

• 30 units

• 25 units

• 35 units

• 20 units

If GF equals x, what is the expression for the length of CF?

• 3x

• 2x

• 4x

• x

If AG is 9x and GD is 5x - 1, what is the value of x?

• 4

• 2

• 1

• 3

What is the total length of AD if AG is 18 units and GD is 9 units?

• 27 units

• 28 units

• 26 units

• 25 units