Download Integrated Geometry - H Constructions and Concurrency Aim

Name: _______________________
Integrated Geometry - H
Date: ___________________
Constructions and Concurrency
Aim: Using what we have learned about constructions, how can we find the four
points of concurrency of triangles?
Do Now:
1. Name the points of concurrency of the:
a. Medians ______________
b. Altitudes _____________
c. Angle Bisectors ____________________
d. Perpendicular Bisectors __________________
2. Which points of concurrency may not always be inside the triangle?
3. Which points of concurrency are always inside the triangle?
Class Work:
1. Construct 3 medians for triangle ABC:
2. Construct 3 altitudes for triangle EDF. (You can extend sides if need be)
Extend each altitude so all three are concurrent.
3.
a) Construct 3 angle bisectors, extend all the bisectors so they are
concurrent with each other.
b) Where the three bisectors are concurrent, put your compass point
here (making it the center), and construct a circle inside the triangle
4.
a) Construct three perpendicular bisectors. Extend each bisector so they
are all concurrent.
b) Make the point of concurrency the center and construct a circle around
the triangle.