[size=150]Your teacher will tell you how to draw and label the [b]medians [/b]of the triangle in the warm-up.[br][size=100][br]After the medians are drawn and labeled, measure all 6 segments inside the triangle using centimeters. [/size][/size]What is the ratio of the 2 parts of each median?[br]

Find the coordinates of the point that partitions segment [math]AN[/math] in a [math]2:1[/math] ratio.[br]

Find the coordinates of the point that partitions segment [math]BL[/math] in a [math]2:1[/math] ratio.[br]

Find the coordinates of the point that partitions segment [math]CM[/math] in a [math]2:1[/math] ratio.[br]

Find the length of [math]AB[/math] in terms of [math]a[/math], [math]b[/math], and [math]c[/math].

[size=150]The goal is to prove that the medians of any triangle intersect at a point. Suppose the vertices of a triangle are [math]\left(0,0\right)[/math], [math]\left(w,0\right)[/math], and [math]\left(a,b\right)[/math].[/size][br][br]Each student in the group should choose 1 side of the triangle. If your group has 4 people, 2 can work together. Write an expression for the midpoint of the side you chose.[br]

Each student in the group should choose a median. Write an expression for the point that partitions each median in a [math]2:1[/math] ratio from the vertex to the midpoint of the opposite side.[br]

Compare the coordinates of the point you found to those of your groupmates. What do you notice?[br]

Explain how these steps prove that the 3 medians of any triangle intersect at a single point.[br]