Constructive Triangles: Second Box: Construction of Quadrilaterals

6-9.

Materials

Box 2 -

• Two blue equilateral triangles
• Two blue right-angled isosceles triangles
• Two blue right-angled scalene triangles
• One blue obtuse-angled scalene triangle
• One blue right-angled scalene triangle (corresponds to the red triangle from Box 1)

Presentation

1. Invite the child to sort the triangles by shape.
2. As before, set aside the two small triangles which correspond to the red ones of the first box.
3. Isolate the two equilateral triangles and invite the child to form all of the possible quadrilaterals.
4.  Try as he might, he can only form one.
5. The child identifies it as the rhombus.
6. Leaving the rhombus intact, the directress takes the two right-angled isosceles triangles and forms the possible figures.
7. The child identifies the figures as they are made.
8. There are two: the square and the common parallelogram.
9. The child may see two different parallelograms.
10. Trace one on a sheet of paper.
11. Form the other and superimpose it.
12. The second parallelogram doesn't fit inside the contours of the first.
13. Trace the second parallelogram and cut out the two figures.
14. By placing the cut-outs back to back, we can see that one is the mirror image of he other, therefore they are the same parallelogram.
15. The child is invited to form the possible quadrilaterals with the two right-angled scalene triangles. <span id="fck_dom_range_temp_1249013966426_509" />
16. The child identifies the three:rectangle, common parallelogram, a different parallelogram.
17. One by one, isolate each type of triangle, ask the child to classify the triangle according to its sides, and ask, "Of how many different lengths are the sides of this triangle?"
18. Conclude that with a triangle whose sides have all one measure, we can form only one figure - the rhombus.
19. With a triangle whose sides have two different measures, we can form to figures - square and common parallelogram.
20. With a triangle whose sides have three different measures, we can form three figures - rectangle and two parallelograms.

Purpose

• To give the relationship between the number of different lengths of the sides and the number of figures which can be possibly constructed.