Exploring real life polygons through GeoGebra

Game Math, 02/12/2025

This book will contain the works of students and teachers within the eTwinning G@ME project.

Indholdsfortegnelse

  1. Team 1. Polygonal fractals - from reality to modeling and personal creations
    1. Jean Monnet HS, Pythagoras tree - Miruna
    2. Jean Monnet HS- Baravelle spiral for parallelogram, Carlos
    3. Gaudeamus_Baravelle Square Spiral_Sofia
    4. CC - Baravelle Square - Carmen Mesías
    5. TS Virovitica - Koch snowflake Emma Ontl 2.m
    6. Gaudeamus_Koch_snowflake_Victoria
    7. Jean Monnet HS- Ana, Fulg
    8. CC - Polygonal Flower - Manuela
    9. Gaudeamus_Sierpinski carpet_Sebastian
    10. Gaudeamus_Baravelle Pentagon Spiral_Mihai
    11. Gaudeamus_Pentagonal flower_Evelina
    12. Gaudeamus_Baravelle Square Spiral_Rada
    13. Gaudeamus_Baravelle Pentagon_Alexandru
    14. Gaudeamus_Baravelli pentagon_Lavinia
    15. Gaudeamus_Pythagoras Tree_Maria
    16. Gaudeamus_Pythagorian tree_Briana
    17. Jean Monnet HS - hexagonalspirals red green - Gugu Rares
    18. Jean Monnet HS- Snowflake - Andrei Balanescu
    19. Jean Monnet HS -Baravelle - hexagonal spiral, Mara
    20. Jean Monnet HS - Sierpinski Carpet - Carlos
    21. Jean Monnet HS, spirals in regular hexagon, Vlad
    22. Jean Monnet hexagonal design -Andrei
    23. Baravelle square - Marta Boncek,2.m
    24. Miruna 2
    25. CC - Sierpinski carpet - Maria Alvarez
    26. CC - Baravelle Square - María Parra
    27. CC - Baravelle Square - VALERIA SPAIN
    28. CC - Koch snowflake - Hugo
    29. CC - Koch snowflake - laura
    30. CC - Sierpinski carpet - Sira Mesias Barrantes
    31. CC - Baravelle Square - MARTA GONZÁLEZ VALENZUELA
    32. CC - Sierpinski carpet - Daniela Barroso Barrera
    33. CC - Baravelle Square - Yanire Morón Sáez
    34. CC - Baravelle Square - Carla Cidoncha
    35. CC - Koch snowflake - diana
    36. CC - Koch snowflake - Coronada
    37. CC - Koch snowflake - Marta González Retamal
    38. CC - Koch snowflake - Cristina
    39. CC - Sierpinski carpet - María Rebollo
  2. Team 2. Polygonal properties illustrated in real life - Worksheets
    1. Jean Monnet HS -Squares in fashion - Maria
    2. Jean Monnet HS, Flower, Ana
    3. Jean Monnet HS - Hexagonal design - problem
    4. Gaudeamus_Sports field _ rectangle_Ana
    5. Gaudeamus_Garden - square_Ana
    6. Gaudeamus_Garden- rhombus_Ana
    7. Gaudeamus_Volley_rectangle_Mădălina
    8. Gaudeamus_tennis_rectangle_Ariadna
    9. Gaudeamus_flag – rectangle_Alexandra
    10. Gaudeamus_Calculating Rye Needed for a Right-Angled Trapezoid Plot_Iustina
    11. Traffic sign, Carlos - Jean Monnet HS - ROMANIA
    12. Jean Monnet HS -Pentagonal Garden -Miruna
    13. Jean Monnet HS - Paving- Rares Gugu
    14. Jean Monnet HS -trapezoidal flower worksheet
    15. Jean Monnet High School -Flower- Sofia
    16. Jean Monnet HS- Spiral - Andrei Tanase
    17. CC - Polygons Real Life - Hugo Nogales
    18. CC - Polygons Real Life -Candela Prat
    19. CC - Polygons Real Life -inma
    20. CC - Polygons Real Life - Hugo
    21. CC - Polygons Real Life - Manuel
  3. Team 3. In the world of polygons - problem solving
    1. Jean Monnet HS - Squares- Rares
    2. Jean Monnet HS - Hexagon with parallelograms
    3. Jean Monnet HS - Miruna, Square
    4. Jean Monnet HS - Christmas house - Luca
    5. Jean Monnet HS, Squares problem, Carlos
    6. Gaudeamus_Teselatii_Rada
    7. Gaudeamus_Teselatii_Lavinia
    8. Gaudeamus_Teselatie_Sebastian
    9. Vlad Popa 2 JM
    10. Pythagoras tree Maria JM
    11. Jean Monnet HS - Baravelle spiral in coordinates, Luca Iancu 7C
    12. Jean Monnet hexagonal design -Andrei
    13. Parallelograms&rectangles JM, Yannis
    14. Jean Monnet HS - rhombus in flower - Daria
    15. SQUARE SUM
  4. Teachers' works
    1. Parallelogram worksheet
    2. Jean Monnet HS worksheet Prob EN rectangle
    3. Trapezoid properties activity
    4. prob EN 2026 JM
    5. CC - Cuadrilateral
    6. CC - Angle Properties of Quadrilaterals

1.

Team 1. Polygonal fractals - from reality to modeling and personal creations

  • 1. Jean Monnet HS, Pythagoras tree - Miruna
  • 2. Jean Monnet HS- Baravelle spiral for parallelogram, Carlos
  • 3. Gaudeamus_Baravelle Square Spiral_Sofia
  • 4. CC - Baravelle Square - Carmen Mesías
  • 5. TS Virovitica - Koch snowflake Emma Ontl 2.m
  • 6. Gaudeamus_Koch_snowflake_Victoria
  • 7. Jean Monnet HS- Ana, Fulg
  • 8. CC - Polygonal Flower - Manuela
  • 9. Gaudeamus_Sierpinski carpet_Sebastian
  • 10. Gaudeamus_Baravelle Pentagon Spiral_Mihai
  • 11. Gaudeamus_Pentagonal flower_Evelina
  • 12. Gaudeamus_Baravelle Square Spiral_Rada
  • 13. Gaudeamus_Baravelle Pentagon_Alexandru
  • 14. Gaudeamus_Baravelli pentagon_Lavinia
  • 15. Gaudeamus_Pythagoras Tree_Maria
  • 16. Gaudeamus_Pythagorian tree_Briana
  • 17. Jean Monnet HS - hexagonalspirals red green - Gugu Rares
  • 18. Jean Monnet HS- Snowflake - Andrei Balanescu
  • 19. Jean Monnet HS -Baravelle - hexagonal spiral, Mara
  • 20. Jean Monnet HS - Sierpinski Carpet - Carlos
  • 21. Jean Monnet HS, spirals in regular hexagon, Vlad
  • 22. Jean Monnet hexagonal design -Andrei
  • 23. Baravelle square - Marta Boncek,2.m
  • 24. Miruna 2
  • 25. CC - Sierpinski carpet - Maria Alvarez
  • 26. CC - Baravelle Square - María Parra
  • 27. CC - Baravelle Square - VALERIA SPAIN
  • 28. CC - Koch snowflake - Hugo
  • 29. CC - Koch snowflake - laura
  • 30. CC - Sierpinski carpet - Sira Mesias Barrantes
  • 31. CC - Baravelle Square - MARTA GONZÁLEZ VALENZUELA
  • 32. CC - Sierpinski carpet - Daniela Barroso Barrera
  • 33. CC - Baravelle Square - Yanire Morón Sáez
  • 34. CC - Baravelle Square - Carla Cidoncha
  • 35. CC - Koch snowflake - diana
  • 36. CC - Koch snowflake - Coronada
  • 37. CC - Koch snowflake - Marta González Retamal
  • 38. CC - Koch snowflake - Cristina
  • 39. CC - Sierpinski carpet - María Rebollo

1.1.

Jean Monnet HS, Pythagoras tree - Miruna

– Game Math

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

1.8.

–

1.9.

–

1.10.

–

1.11.

–

1.12.

–

1.13.

–

1.14.

–

1.15.

–

1.16.

–

1.17.

–

1.18.

–

1.19.

–

1.20.

–

1.21.

–

1.22.

–

1.23.

–

1.24.

–

1.25.

–

1.26.

–

1.27.

–

1.28.

–

1.29.

–

1.30.

–

1.31.

–

1.32.

–

1.33.

–

1.34.

–

1.35.

–

1.36.

–

1.37.

–

1.38.

–

1.39.

–

2.

Team 2. Polygonal properties illustrated in real life - Worksheets

  • 1. Jean Monnet HS -Squares in fashion - Maria
  • 2. Jean Monnet HS, Flower, Ana
  • 3. Jean Monnet HS - Hexagonal design - problem
  • 4. Gaudeamus_Sports field _ rectangle_Ana
  • 5. Gaudeamus_Garden - square_Ana
  • 6. Gaudeamus_Garden- rhombus_Ana
  • 7. Gaudeamus_Volley_rectangle_Mădălina
  • 8. Gaudeamus_tennis_rectangle_Ariadna
  • 9. Gaudeamus_flag – rectangle_Alexandra
  • 10. Gaudeamus_Calculating Rye Needed for a Right-Angled Trapezoid Plot_Iustina
  • 11. Traffic sign, Carlos - Jean Monnet HS - ROMANIA
  • 12. Jean Monnet HS -Pentagonal Garden -Miruna
  • 13. Jean Monnet HS - Paving- Rares Gugu
  • 14. Jean Monnet HS -trapezoidal flower worksheet
  • 15. Jean Monnet High School -Flower- Sofia
  • 16. Jean Monnet HS- Spiral - Andrei Tanase
  • 17. CC - Polygons Real Life - Hugo Nogales
  • 18. CC - Polygons Real Life -Candela Prat
  • 19. CC - Polygons Real Life -inma
  • 20. CC - Polygons Real Life - Hugo
  • 21. CC - Polygons Real Life - Manuel

2.1.

Jean Monnet HS -Squares in fashion - Maria

With the data in the attached figure, find the side of the square KLMN
With the data in the attached figure, find the equation of the line ML
With the data in the attached figure, find the equation of the line MN
With the data in the attached figure, find the area of the square GHIJ.
– Game Math

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

2.7.

–

2.8.

–

2.9.

–

2.10.

–

2.11.

–

2.12.

–

2.13.

–

2.14.

–

2.15.

–

2.16.

–

2.17.

–

2.18.

–

2.19.

–

2.20.

–

2.21.

–

3.

Team 3. In the world of polygons - problem solving

  • 1. Jean Monnet HS - Squares- Rares
  • 2. Jean Monnet HS - Hexagon with parallelograms
  • 3. Jean Monnet HS - Miruna, Square
  • 4. Jean Monnet HS - Christmas house - Luca
  • 5. Jean Monnet HS, Squares problem, Carlos
  • 6. Gaudeamus_Teselatii_Rada
  • 7. Gaudeamus_Teselatii_Lavinia
  • 8. Gaudeamus_Teselatie_Sebastian
  • 9. Vlad Popa 2 JM
  • 10. Pythagoras tree Maria JM
  • 11. Jean Monnet HS - Baravelle spiral in coordinates, Luca Iancu 7C
  • 12. Jean Monnet hexagonal design -Andrei
  • 13. Parallelograms&rectangles JM, Yannis
  • 14. Jean Monnet HS - rhombus in flower - Daria
  • 15. SQUARE SUM

3.1.

Jean Monnet HS - Squares- Rares

– Game Math

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

3.9.

–

3.10.

–

3.11.

–

3.12.

–

3.13.

–

3.14.

–

3.15.

–

4.

Teachers' works

  • 1. Parallelogram worksheet
  • 2. Jean Monnet HS worksheet Prob EN rectangle
  • 3. Trapezoid properties activity
  • 4. prob EN 2026 JM
  • 5. CC - Cuadrilateral
  • 6. CC - Angle Properties of Quadrilaterals

4.1.

Parallelogram worksheet

A father owns a garden shaped like a parallelogram. He throws a coin at a point inside the garden and connects this point to the four vertices of the parallelogram, obtaining four triangles.[br][br]The father decides that one son will inherit two opposite triangles, and the other son will inherit the remaining two triangles.[br][br]One of the sons is unhappy and claims that the division is unfair.[br][br][b]Is he right? Justify your answer.[/b]
Step 1
Move the cursor to Step 1 to construct the height of the triangle PCD: PE perpendicular to CD
Step 2
Move the cursor to Step 2 to construct the height of the triangle PAB: PF perpendicular to AB.
Calculate the area of ​​triangle PCD.
Calculate the area of ​​triangle PAB.
Calculate the sum of the areas of ​​triangleS PAB and PCD.
Conclusion
Is the unhappy son right? Why?
– Game Math

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

Information