In my investigation, I will construct a medial triangle. The definition of a medial triangle is determine the midpoints of all three sides of the triangles and then connect the midpoints and then you have your medial triangle.

 

INVESTIGATION:

Here's starting triangle

I will now construct the midpoints of each side of the triangle.

The midpoint of line segment AB is point H. The midpoint of line segment AC is point F. The midpoint of line segment BC is G.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I will now show that by connecting the midpoints of the three sides of the triangle, will give the medial triangle.

I will now show that by definition of the medial triangle the inscribed triangle known as the medial triangle should be equal to all other triangles inscribed within the triangle. The area of all four triangles should be equal to each other.