More on Triangles: Lesson Three


Big Idea – We can describe, measure, and compare spatial relationships.

  • to build on students' knowledge of triangle and develop students' reasoning with properties of different classes of triangles
  • to develop students' language related to the formal geometric names of scalene, isosceles, and equilateral triangles
  • to engage students in the process of defining triangles/geometric shapes which is useful in their subsequent work in proposing definitions of other mathematical concepts (e.g., quadrilaterals)
  • to highlight inclusive relations between triangles (e.g., recognizing equilateral triangles as special types of isosceles triangles)

    Overarching Aims:

    Informal descriptions of properties that coordinate their visual impressions with geometric language.
  • Properties of movement:
    - Students may notice that some points can be dragged directly and move freely, that some cannot be grabbed but may move by means of another point.
    - You may hear students say words like ‘paralyzed’ triangle for isosceles and equilateral triangles after noticing the restrictive movements of these triangles upon dragging.
  • Properties of symmetry:
    - Students may notice symmetry in the isosceles and equilateral triangles and non-symmetry in the scalene triangles

    Informal recognition of these properties may be helpful in recognizing formal geometric properties like symmetrical movement, equal angles, and equal sides.


You'll be using Sketches 5 and 6 of this file to explore which coloured triangles could fit into the given triangle outlines.

The intent of these two sketches is to make explicit comparisons between the pairs of different types of triangles.

Each triangle type has a different colour (pink for scalene, red for equilateral, blue for isosceles), which allows you and the students to begin referring to the triangles by their formal geometric names.

Key questions to pose for both sketches are:

  • Can you make a prediction?
  • Why do you think that happens?

Sketch 5 – Comparison 1
Sketch 6 – Comparison 2

Activity – Whole Group

Working with Sketch 5

  1. Project Sketch 5 on the screen.
  2. Introduce the term scalene (pink triangle) and equilateral (outline).
  3. Have one student drag the scalene triangle to review its properties.
  4. Have the students predict whether the scalene triangle will fit into the equilateral outline.
  5. Now have a student explore trying to overlap the pink scalene triangle onto the equilateral outline.
  6. Repeat the process for the red equilateral triangle in the bottom half of Sketch 5.

Working with Sketch 6

  1. Project Sketch 6 on the screen.
  2. Review the term equilateral (red triangle) and introduce the term isosceles (outline).
  3. Have the students predict whether the equilateral triangle will fit into the isosceles outline.
  4. Now have the students explore trying to overlap the red equilateral triangle onto the isoscleles outline.
  5. Repeat the process for the blue isosceles triangle in the bottom half of Sketch 6.