Incenter Exploration (B)
- Author:
- mlute, Tim Brzezinski
- Topic:
- Circle
3 or more lines are said to be concurrent if and only if they intersect at exactly one point.
The angle bisectors of a triangle's 3 interior angles are all concurrent.
Their point of concurrency is called the INCENTER of the triangle.
In the applet below, point I is the triangle's INCENTER.
Use the tools of GeoGebra in the applet below to complete the activity below the applet.
Be sure to answer each question fully as you proceed.
Directions:
1) Click the checkbox that says "Drop Perpendicular Segments from I to sides.
2) Now, use the Distance tool to measure and display the lengths IG, IH, and IJ. What do you notice?
3) Experiment a bit by moving any one (or more) of the triangle's vertices around
Does your initial observation in (2) still hold true? Why is this?
4) Do the angle bisectors of a triangle's interior angles also bisect the sides opposite theses angles?
Use the Distance tool to help you answer this question.
5) Is it ever possible for a triangle's INCENTER to lie OUTSIDE the triangle
If so, under what condition(s) will this occur?
6) Is it ever possible for a triangle's INCENTER to lie ON the triangle itself?
If so, under what condition(s) will this occur?