Presentation of Concepts: Similarity

Age

6-9.

Materials

• Metal insets of the square and its subdivisions
• A red cardboard rectangle 20 x 2.5 cm
• Metal insets of the triangles
• Geometry charts: S9, T5
  

Presentation

1. Discuss the meaning of the word similar and give examples of things resembling one another, having the same traits, but different in other ways (similar).
2. Isolate the whole inset and the inset of the square 1/4.
3. Ask the child to identify their shapes.
4. They have the same name. are they congruent?
5. Superimpose to find out.
6. Hold up the small square while the child walks away with the large square to see that they look alike.
7. These two figures are similar.
8. All squares are similar simply by their definition.
9. Isolate the 1/2 and 1/8 pieces and identify their shapes as rectangles.
10. They have the same name.
11. Recall the nomenclature - sides, base, height, angles. superimpose the angles to show that the angles are equal.
12. Place two small rectangles adjacent to the larger rectangle to show that the base of the larger is twice the base of the smaller.
13. Repeat the experiences in reference to the height.
14. Thus, these two rectangles are similar to each other because their angles are respectively equal and the sides are in proportion to one another: the base and height of the larger are double those of the smaller.
15. Here the name was not sufficient to determine similarity, nor are equal angles sufficient; the sides must be proportionate.
16. Repeat the experience with two triangular fractional pieces: 1/2, 1/8.
17. Classify them.
18. Superimpose the angles.
19. Use an extra 1/8 to demonstrate that the sides are proportionate.
20. Note: All square by their definition are similar to each other.
21. Rectangles however must have proportionate sides.
22. Compare the cardboard rectangle - 20 x 2.5cm to the 1/2 rectangle inset to see the extreme case of two non-similar rectangles.
23. The base of the metal rectangle is twice the base of the other, while the height of the metal rectangle is half the height of the other.
24. (Triangle) Isolate the 1/2 triangle inset and classify it.
25. Draw another right-angled scalene triangle which is not similar to show that the classification is not enough to render them similar.
26. Bring out a 1/3 inset and classify it.
27. These two triangles (1/2 and 1/3) have nothing in common.
28. Show that the small triangle (1/4) which has the same name as the whole triangle (and thus, has equal angles) also has proportionate sides.
29. Like the square which is the perfect quadrilateral, the equilateral triangle, which is the perfect triangle, is similar to all other equilateral triangles by its definition.