Geometry 4-A-1 Categorizing Two Dimensional Figures

I would present triangles to the students after talking about the definition of a polygon.  I would first have them define the different types of triangles in their own words.  This would let me know their prior knowledge of triangles.

Triangle: A polygon with 3 sides.

Triangles (classified by sides)

Equilateral Triangle:  A triangle with 3 congruent sides.

Isosceles Triangle:  A triangle with 2 congruent sides.

Scalene Triangle:  A triangle with no congruent sides.

Triangles (classified by angles)

Right triangle:  A triangle with one angle equal to 90°.

Acute triangle:  A triangle where all angles are less than 90°.

Obtuse triangle:  A triangle where one angle is greater than 90°.

I would first have them explore the characteristics of each triangle.  Some questions:

• Is it possible to have 2 right angles in a right triangle? Why or why not?
• Explain if all angles have to be less than 90° in an acute triangle, why or why not.  Illustrate your observations.
• Can you draw an obtuse triangle that have 2 angles greater than 90°?  Explain your answer.
• Is it possible for an isosceles triangle to be equilateral, or an equilateral triangle to be isosceles?  Why or why not?
• What can we determine about the angles of an equilateral, isosceles, and scalene triangle?  Illustrate your findings.  Why is this important to know?

I would then have the students compare the triangles, look for similarities and differences among them.  We would look at a variety of triangles and have them experiment with classifying them.  My objective would be for the student to obtain the knowledge that every triangle can be classified by its angles and by its sides. They could explain their knowledge by drawing a diagram to illustrate all possible ways a triangle can be categorized by its sides and angles.  At the end, revisit their first definitions and change what they have discovered.  A journal entry would also be a nice way to collaborate all the ideas they have developed in their discoveries.