To start our next lesson, let's begin by writing the standard at the top of our notes.
LT5.3 - I can use properties of medians and centroids in triangles.
This lesson will be about more special segments in triangles - medians, and their special point - the centroid. Let's start by defining these in our packets.
Medians - Segments that connect a vertex in a triangle with the midpoint of the opposite side.
Just like perpendicular bisectors and angle bisectors like we've already studied, it turns out that medians also intersect at a single point!! The point where all three medians intersect is called the centroid.
Let's click through the applet below to understand how the centroid is found and find out what's special about it...

The special relationship that goes with the centroid is explained in Theorem 5.7, the Centroid Theorem. Copy the diagram above into the third column of your packet for this theorem.
Theorem 5.7: Centroid Theorem - The medians of a triangle intersect at a point called the centroid that is two thirds of the distance from each vertex to the midpoint of the opposite sides.
Let's move on to the next workbook to play around with the Centroid more. Answer the big idea questions in your notebook before moving on to the practice to check your understanding.