This document discusses counting triangles using fundamental counting principles. It contains examples of counting the number of triangles that can be formed with different numbers of vertices. For example, it shows that the number of triangles that can be formed using 5 vertices is 15. It also contains practice problems asking to count triangles with given numbers of vertices and provides the solutions. The document is about mathematical properties and counting principles for geometry situations.

1. SITUACIONES GEOMETRICAS
CONTEO DE TRIANGULOS
DEMETRIO CCESA RAYME
3º DE SECUNDARIA
ÁREA : MATEMÁTICA
SEMANA 33
EXPERIENCIA Co. : Nº9
ACTIVIDAD Ap. : Nº6
PROGRESIONES

2. 1.

3. Propiedad Fundamental de Conteo D
1.

4. 1.

5. 1.

6. Propiedad Fundamental de Conteo D
2.

7. 2.

8. 2.

9. 3.

10. 3.

11. 7.
4.

12. 7.
4.

13. 5.

14. 5.

15. 6.
a) 144 b) 160 c) 175 d) 180

16. a) 144 b) 160 c) 175 d) 180
6.

17. 11.
Propiedad Fundamental de Conteo D
3.

18. 11.
7.

19. 11.7.
Nº D =
5(5+1)
2
=
5(6)
2
= 15
2
3
5
4
1

20. 8.

21. 8.

22. 9.

23. 9.
Nº D =
9(9+1)
2
=
9(10)
2
= 45
1
2
4
3
5
6
7
8
9

24. 10.

25. 10.
Nº D = (
6(6+1)
2
).2 = 21 . 2 = 42

26. Propiedad Fundamental de Conteo D
1 2 3 4 ……. n
Nº D =
𝑚𝑛(𝑚 + 𝑛)
2
4.

27. 11.
11.
a) 56 b) 58 c) 60 d) 62

28. 11.
11.
Nº D =
3.5(3+5)
2
=
15(8)
2
= 60
a) 56 b) 58 c) 60 d) 62

29. 11.
12.
a) 80 b) 85 c) 88 d) 90

30. 11.
12.
a) 80 b) 85 c) 88 d) 90
Nº D =
4.5(4+5)
2
=
20(9)
2
= 90

31. 11.
13.
a) 30 b) 35 c) 40 d) 45

32. 11.
13.
a) 30 b) 35 c) 40 d) 45
Nº D =
2.5(2+5)
2
=
10(7)
2
= 35