Archive for March 2014

EXTERIOR ANGLE THEOREM (Part 2: Proof)


Here is the two-column proof for the EXTERIOR ANGLE THEOREM. You may download and print it for your perusal.


Your comments and suggestions are welcome here. You may write them in the comment box below. 

EXTERIOR ANGLE THEOREM (Part 1: Exploration)

mathematics,angles,geometry,acute triangle,interior angles,IGCSE

Many are already familiar with the angles of a triangle. Many can easily point out which are the interior angles and even draw the exterior angles.

On the other hand, how many are you are familiar with the exterior angle theorem? What is the relationship of the exterior angles with the interior angles? The answer for these questions can be summarized by the "Exterior Angle Theorem".

In this post, let us discover where this theorem come from by using some illustrative examples.

Materials needed:  ruler, protractor, calculator and pencil

Procedure:
1) On a piece of paper, draw one (1) acute triangle, one (1) right triangle, and one (1) obtuse triangle. Name each triangle as triangle ABC, with AC as the base.
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2) Extend the base of AC to a point D. Points A, C and D should be on the same line and C is between A and D.
mathematics,angles,geometry,acute triangle,interior angles,IGCSE

mathematics,angles,geometry,right triangles,interior angles,IGCSE

mathematics,angles,geometry,interior angles,obtuse triangles,IGCSE
  • angle BCD is the exterior angle of each triangle
  • angles A and B are the remote (non-adjacent) interior angles of each triangle
3) Measure each of the angles and complete the table below:
mathematics,angles,geometry,interior angles,IGCSE

4) Look at the rightmost part of the table. Compare the sum of the measures of angles A and B and the exterior angle. 
mathematics,angles,geometry,acute triangles,interior angles,IGCSE

mathematics,angles,geometry,right triangles,interior angles,IGCSE

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5) We can now make a conclusion/generalization about the relationship of the measurement of the exterior angle and the remote interior angles.
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Here is the pdf copy of the activity, if to be conducted in a classroom setting. You are free to download it and use for your class. Hope it will be beneficial for you.

Your comments and suggestions are accepted here. Just write them in the comment box below. Thank you!  



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