1. Medians and Altitudes of triangles. Unit 3 Concept 3

2. Materials for TODAY • 3 pieces of PATTY paper • Pencil • 2 markers • Compass…makes circles… • Handouts for today.

3. Folding Perpendicular bisectors • On one piece of patty paper, draw an acute triangle. • Outline your triangle in marker. • Label the vertices A, B, and C • On the next piece of PATTY paper, draw an obtuse triangle. • Outline it in marker • Label the vertices, A, B, and C • On the 3rd piece of Patty paper draw a RIGHT triangle and follow the directions above.

4. Follow teacher directions for folding. • Fill in your scrap book page for perpendicular bisectors and the CIRCUMCENTER.

5. Medians of a Triangle • A median of a triangle is a segment that extends from a vertex to the midpoint of the opposite side. • The medians intersect at one point (Point of concurrency) called the centroid. • The centroid is located 2/3 of the way down the median.

6. Let’s look at some examples… • C is the centroid of ∆GHJ and CM = 8. Find HM and CH. H C J G M

7. More… • C is still the centroid of the triangle below. IF GC = 10, what is the length of CI and GI? • IF KJ = 12, what is the length of JC and KC? H I K C J G M

8. Altitudes of a triangle • An altitude in a triangle, is a segment that extends from a vertex and is perpendicular to the opposite side or the line that contains the opposite side. The point of concurrency for the altitudes is called the orthocenter. It is sometimes inside, sometimes outside and sometimes on the triangle.

9. Perpendicular Bisectors of a Triangle • The perpendicular bisector of a side of a triangle is a segment or line that contains the midpoint of that side and is perpendicular to that side. Sketchpad demo.

10. Perpendicular bisectors of a triangle • The point of concurrency for the perpendicular bisectors of a triangle is called the circumcenter. • The circumcenter of a triangle is equidistant from each vertex of the triangle.