Angular bisectors and incenter of a triangle

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The intersecting point of three lines which are the bisectors of three angles of a triangle that is the incenter and it's properties are examined.

Objectives

Introduce angular bisectors in a triangle and their point of concurrence.

Estimated Time

40 minutes.

Prerequisites/Instructions, prior preparations, if any

Angles, angle bisectors , concurrent lines and triangles should have been covered.

Materials/ Resources needed

Digital resources: Laptop, projector and a pointer.

Geogebra file: Concurrency of angular bisectors.ggb


Download this geogebra file from this link.


Process (How to do the activity)

  1. The teacher can use this geogebra file and ask the questions listed below.
  • Developmental Questions;
  1. What type of triangle is this ? Why ?
  2. Identify the three angles.
  3. What is an angle bisector ?
  4. Identify the point of concurrence of angle bisectors ?
  5. This point, called incentre of the triangle does its position change with the type of triangle ?
  6. Identify the circle. What is its radius ? What can this radius be called ?
  7. What is this circle called ?
  • Evaluation:
  1. What is incentre, inradius and incircle ?
  • Question Corner:
  1. What do you think would be the practical applications of the incentre and incircle ?