Understanding Triangle Medians and Centroids

The video tutorial explains the properties of medians and centroids in a triangle, demonstrating how to calculate the area of smaller triangles formed by medians. It covers the calculation of the area of triangle BGC by dividing the larger triangle into six equal-area triangles. The tutorial also explains how to find the length of AG using the centroid's property of dividing medians in a 2:1 ratio. Finally, it calculates the area of triangle FGH using altitudes and similarity arguments.

What is the significance of the centroid in a triangle?

• It is the point where all altitudes meet.

• It is the point where all medians meet.

• It is the point where all perpendicular bisectors meet.

• It is the point where all angle bisectors meet.

How many smaller triangles of equal area do the medians divide a triangle into?

• Six

• Nine

• Four

• Three

If the area of triangle AEC is 108, what is the area of triangle BGC?

• 36

• 24

• 18

• 12

What is the ratio in which the centroid divides each median?

• 1:2

• 1:1

• 2:1

• 2:3

If AD is 15, what is the length of AG?

• 5

• 7.5

• 10

• 12.5

What is the altitude of triangle FGE if its base is 6 and area is 18?

• 3

• 4

• 6

• 5

How can the length of FH be determined if AH is 8 and AF is 6?

• FH = AH * AF

• FH = AH + AF

• FH = AH - AF

• FH = AF - AH

What is the area of triangle FGH if FH is 2 and GH is 6?

• 8

• 10

• 4

• 6

Which of the following is a method to find the length of HG?

• Using the law of cosines

• Using the law of sines

• Using the similarity of triangles

• Using the Pythagorean theorem

What is the length of HG if it is 2/3 of 9?

• 3

• 4

• 5

• 6