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.