Exploring the Median of a Triangle

This video tutorial explains the concept of medians in a triangle, defining them as line segments from a vertex to the midpoint of the opposite side. It covers the properties of medians, including their role as segment bisectors and their concurrency at the centroid, which acts as the triangle's center of gravity. The video also discusses how medians divide triangles into smaller triangles of equal area and provides algebraic examples to calculate median lengths using equations.

What is a median in a triangle?

• A line segment from the midpoint of one side to the midpoint of another side

• A line segment that bisects an angle

• A line segment from a vertex to the opposite vertex

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

How many medians does a triangle have?

• One

• Two

• Three

• Four

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

• Incenter

• Orthocenter

• Centroid

• Circumcenter

What is the centroid of a triangle?

• The point where the angle bisectors meet

• The point where the perpendicular bisectors meet

• The point where the altitudes meet

• The point where the medians meet

What is a key property of the medians in terms of the area they divide?

• They divide the triangle into two smaller triangles of equal area

• They do not affect the area of the triangle

• They divide the triangle into three smaller triangles of equal area

• They divide the triangle into four smaller triangles of equal area

If AE is a median and AE = 9, what is the length of AP?

• 3

• 6

• 12

• 9

If PD is 4, what is the length of BP?

• 8

• 2

• 12

• 4

If BP = 10x - 4 and PD = 3x + 2, what is the length of the median BD?

• 24

• 16

• 32

• 27

What is the relationship between BP and PD?

• BP is half of PD

• BP is three times PD

• BP is equal to PD

• BP is twice PD

If PD = 4x - 7 and BD = x^2 + 11, what are the possible values of BP?

• 18 or 50

• 16 or 32

• 12 or 24

• 8 or 16