Altitudes and orthocenter of a triangle

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An altitude of a triangle is a line segment that is drawn from the vertex to the opposite side and is perpendicular to the side.  A triangle can have three altitudes. Point of intersection of these lines for different types of triangles is explored.

Objectives

Introduce altitudes of a triangle and their point of concurrence.

Estimated Time

30 minutes

Prerequisites/Instructions, prior preparations, if any

Types of triangles and concept of altitudes should have been covered.

Materials/ Resources needed

Digital resources: Laptop, geogebra file, projector and a pointer.

Geogebra resources: Concurrency of altitudes.ggb


Download this geogebra file from this link.


Process (How to do the activity)

  1. Project the geogebra file and ask the following questions.
  • Developmental Questions:
  1. Which type of triangle is this ?
  2. What is an altitude ?
  3. How do we construct an altitude ?
  4. What is the point of concurrence of 3 altitudes called ?
  5. Identify the position of point of concurrence in different triangles.
  • Evaluation:
  1. What are the positions of orthocentre in different types of triangles.
  • Question Corner:
  1. Find the applications of orthocentre.