Constructing the Orthocenters and Centroids of Triangles

I know that I didn't get to do this in class today but I am going to assign it anyway because there are directions on og 332 on how to construct an altitude of a triangle as well as a median of a triangle. If you have trouble following the directions, go to Youtube and do a search on how to construct the median of a triangle and how to construct the altitude of a triangle. There are numerous videos out there. I know. I've done the search myself.

orthocenter:

• point of concurrency


• 3 altitudes of a triangle

circumcenter

• point of concurrency


• 3 medians of a triangle

Follow the instructions on pg 332 to complete the following:

Construct:

1. the orthocenter of an acute scalene triangle



2. the orthocenter of an obtuse triangle



3. the orthocenter of a right triangle



4. the centroid of acute scalene triangle



5. the centroid of of an obtuse triangle



6. the centroid of a right triangle



7. circumscribe a circle about an acute triangle



8. circumscribe a circle about an obtuse triangle



9. inscribe a circle in an acute triangle (remember, you MUST construct a perpendicular from the incenter to any side (preferably the longest side) of a triangle first BEFORE you can inscribe a circle!!!!)



10. inscribe a circle in an obtuse triangle

Constructing the Circumcenters and Incenters of different types of triangles

Construct the:

1. circumcenter of an acute triangle; then circumscribe a circle about the triangle



2. circumcenter of an obtuse triangle; then circumscribe a circle about the triangle



3. circumcenter of a right triangle; then circumscribe a circle about the triangle



4. incenter of an acute triangle; then inscribe a circle in the triangle (don't forget to construct a perpendicular to the longest side of the triangle first!)



5. incenter of an obtuse triangle; inscribe a circle



6. incenter of a right triangle; inscribe a circle

if you are even the tiniest bit off, do it over again!!!!!! PERFECTION is what you are striving for in a construction!!!!

please use colored pencils and/or highlighters to help you identify the different perpendicular bisectors and angle bisectors in your constructions. no color = no bueno =(