The document discusses different geometric properties of triangles including medians, centroids, and altitudes. A median is a segment from a vertex to the midpoint of the opposite side. The three medians of a triangle intersect at the centroid, which divides each median into segments with a ratio of 2:1. An altitude is a segment drawn from a vertex perpendicular to the opposite side, and can be inside, on, or outside the triangle depending on if the triangle is acute, right, or obtuse.

1. Lil’ Wayne Sez Most things in Geometry make perfect sense…. … .it’s just hard to explain them.

2. Today we will go over the definitions, but then Mr. A will draw them LIVE Check this out!

3. A Median is a segment that has endpoints at a vertex and the midpoint of the opposite side in a triangle. a triangle has three of these as well. MEDIAN !!

4. And, of course, there’s a special name for where the medians meet… CENTROID.

5. Centroid The medians of a triangle are concurrent (all intersect) at a point that divides each median into two segments, one of which is twice as long as the other. The point of concurrency is called the centroid . Also called the center of gravity or center of balance .

6. What’s special about the centroid , Mr. A ?

7. I’m Glad You Asked! The Centroid is always 2/3 of the total distance from the vertex to the other side! 2/3

8. For Example: If G is the centroid, and GE = 6 , how long is BE ? A B C D E F G GE = (2/3)BE 6 = (2/3)BE 6(3/2) = BE 9 = BE

9. Altitudes Altitude of a Triangle – An altitude is a segment drawn from the vertex of a triangle perpendicular to the opposite side. Can be inside, on a side, or outside the traingle Acute Triangle: Altitude inside Right Triangle: Altitude is a side Obtuse Triangle: Altitude outside

10. The altitude is a segment from the vertex of a triangle to the opposite side that is perpendicular to that side. ORTHOCENTER