Triangle Medians and Length Relationships

The video tutorial explains the concept of a centroid in a triangle, where the three medians intersect. It describes what a median is and how it connects a vertex to the midpoint of the opposite side. The tutorial highlights the interesting property of medians being divided into a 1/3 and 2/3 ratio by the centroid. It provides examples to illustrate how to calculate the lengths of different segments of the medians using this ratio. The video also clarifies how to identify which segment is 1/3 and which is 2/3 based on their position relative to the vertex and the centroid.

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

• Centroid

• Circumcenter

• Orthocenter

• Incenter

A median in a triangle is drawn from a vertex to which point on the opposite side?

• Circumcenter

• Centroid

• Midpoint

• Any point

If AE is a median, what can be said about segments AF and FE?

• AF is unrelated to FE

• AF and FE are congruent

• AF is twice FE

• AF is half of FE

How is a median divided by the centroid?

• Into quarters

• Into halves

• Into one-third and two-thirds

• Equally

If the length of RD is known, how can you find the length of BR?

• Divide RD by 2

• Double RD

• Subtract RD from the total median length

• Multiply RD by 3

What is the relationship between CR and FR if FR is 5?

• CR is half of FR

• CR is equal to FR

• CR is double FR

• CR is unrelated to FR

Which part of the median is longer, from the vertex to the centroid or from the centroid to the opposite side?

• Vertex to centroid

• Centroid to opposite side

• Both are equal

• Depends on the triangle

If a median is divided into one-third and two-thirds, which segment is closer to the vertex?

• One-third

• Two-thirds

• Both are equal

• Depends on the triangle

If AR is 8, what is the length of RA?

• 8

• 16

• 4

• 12

What is the total length of AE if AR is 8 and RA is 4?

• 14

• 8

• 10

• 12