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Methodical recommendation:
Theory
| Number | Name | Description |
|---|---|---|
| 1. | Introduction | Get introduced to the concept of Thales theorem. |
| 2. | Basic proportionality or Thales theorem | Let us learn the basic proportionality theorem or Thales theorem. |
| 3. | Angle bisector theorem and its converse | Learn the concept of angle bisector theorem and its converse. |
| 4. | Types of construction of triangle | Learn the different types of construction of a triangle and also learn how to construct a segment of a circle on a given line segment. |
| 5. | Construction of a triangle when its base, vertical angle and median are given | Learn how to construct a triangle if its base, vertical angle and the median from the vertex of the base are given. |
| 6. | Construction of a triangle when its base, vertical angle and altitude are given | Learn how to construct a triangle when its base, vertical angle and the altitude from the vertex to the base are given. |
| 7. | Construction of a triangle if its base, vertical angle and the point on the base are given | Learn how to construct a triangle if its base, vertical angle and the point on the base where the bisector of the vertical angle meets the base are given. |
Textbook Questions
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Multiple choice question | Other | easy | 2 m. | Check your understanding skills in the concept of Thales theorem. |
| 2. | Two mark example problems I | Other | medium | 4 m. | Select the correct answer using theorems. |
| 3. | Two mark example problems II | Other | medium | 2 m. | Work on the problem to find the answers using Thales theorem or angle bisector theorem. |
| 4. | Two mark exercise problems I | Other | medium | 2 m. | In this exercise, find the lengths of the sides of triangle ABC. |
| 5. | Two mark exercise problems II | Other | medium | 4 m. | Work on the problem to find the answers using Thales theorem or angle bisector theorem. |
| 6. | Two mark exercise problems III | Other | medium | 0 m. | In this exercise, prove the given statement using theorems. |
| 7. | Five mark example problems I | Other | medium | 5 m. | In this exercise, find the lengths of the sides of triangle ABC. |
| 8. | Five mark example problems II | Other | medium | 5 m. | Try to answer the questions using theorems. |
| 9. | Five mark exercise problems I | Other | medium | 5 m. | In this exercise, find the lengths of the sides of triangle ABC. |
| 10. | Five mark exercise problems II | Other | medium | 5 m. | Try to answer the questions using theorems. |
| 11. | Five mark exercise problems III | Other | medium | 5 m. | Try to answer the questions using theorems. |
| 12. | Five mark exercise problems IV | Other | medium | 0 m. | In this exercise, prove the given statement using theorems. |
| 13. | Five mark exercise problems V | Other | medium | 0 m. | In this exercise, prove the given statement using theorems. |
| 14. | Five mark exercise problems VI | Other | medium | 0 m. | Try to prove the given statement by applying the theorem. |
| 15. | Five mark exercise problems VII | Other | medium | 0 m. | Try to prove the given statement by applying the theorem. |
| 16. | Five mark exercise problems VIII | Other | hard | 0 m. | Try to prove the given statement by applying the theorem. |
| 17. | Five mark exercise problems IX | Other | hard | 5 m. | Find the required by applying the thales theorem. |
| 18. | Five mark exercise problems X | Other | hard | 0 m. | Find the required by applying the thales theorem. |
| 19. | Eight mark example problems I | Other | hard | 0 m. | Try to construct a triangle when its base, the vertical angle and the median from the vertex of the base are given. |
| 20. | Eight mark example problems II | Other | hard | 0 m. | Try to construct a triangle when its base, the vertical angle and the altitude from the vertex to the base are given. |
| 21. | Eight mark example problems III | Other | hard | 0 m. | Try to construct a triangle when its base, the vertical angle and the point on the base where the bisector of the vertical angle meets the base. |
| 22. | Eight mark exercise problems I | Other | hard | 0 m. | Practive how to construct a triangle if its base, vertical angle and the point on the base where the bisector of the vertical angle meets the base are given. |
| 23. | Eight mark exercise problems II | Other | hard | 0 m. | Practive how to construct a triangle if its base, vertical angle and the point on the base where the bisector of the vertical angle meets the base are given. |
| 24. | Eight mark exercise problems III | Other | hard | 0 m. | Try to construct a triangle when its base, the vertical angle and the median from the vertex of the base are given. |
| 25. | Eight mark exercise problems IV | Other | hard | 0 m. | Try to construct a triangle when its base, the vertical angle and the altitude from the vertex to the base are given. |
| 26. | Eight mark exercise problems V | Other | hard | 0 m. | Try to construct a triangle when its base, the vertical angle and the altitude from the vertex to the base are given. |
| 27. | Eight mark example problems VI | Other | hard | 0 m. | Try to construct a triangle when its base, the vertical angle and the point on the base where the bisector of the vertical angle meets the base. |
Practice Questions
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Calculate the side AD of triangle ABC | Other | easy | 1 m. | Apply the theorem and determine the side EC of the given triangle. |
| 2. | Determine the side CB of triangle ABC | Other | easy | 3 m. | Apply the theorem and determine the side CB of the given triangle. |
| 3. | Calculate the value of the variable | Other | easy | 3 m. | Apply the theorem and find the value of the variable. |
| 4. | Find the length of AE of triangle ABC | Other | easy | 3 m. | Practice a problem by applying the theorem and find the value of AE. |
| 5. | Determine the value of the variable | Other | medium | 4 m. | Apply the theorem and find the value of the variable. |
| 6. | Find the side length of the triangle | Other | medium | 4 m. | Apply the theorem and determine the side length of the triangle. |
| 7. | Check whether the lines of the triangle are parallel | Other | medium | 4 m. | Practice a problem to verify the statement by applying the theorem. |
| 8. | Determine the length of PM | Other | medium | 4 m. | Check your understanding skills in the concept of solving problems by applying theorems. |
| 9. | Calculate the length of PT and VQ | Other | medium | 4 m. | Apply the theorem and find the length of PT and VQ. |
| 10. | Check whether CD is the bisector of angle C | Other | medium | 4 m. | Practice a problem to verify the statement by applying the theorem. |
| 11. | Observe the picture and answer the questions | Other | hard | 6 m. | Check your understanding skills in the concept of Thales theorem. |
| 12. | Determine the height of the small tree | Other | hard | 5 m. | Check your understanding skills in the concept of Thales theorem. |
| 13. | Calculate the height of the mother | Other | hard | 5 m. | Check your understanding skills in the concept of Thales theorem. |
| 14. | Verify the trees are parallel | Other | hard | 5 m. | Practice a problem to verify the statemet by applying the theorem. |
Key Questions for School Exam Preparation
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Answer the following questions | Other | hard | 9 m. | In this exercise, find the lengths of the sides AB and AC. |
| 2. | Prove the following | Other | medium | 2 m. | Work on the problem to find the answers using Thales theorem or angle bisector theorem. |
Questions for Teacher Use
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Angle bisector theorem | Other | easy | 4 m. | Apply the theorem and find the value of the variable. |
| 2. | Thales theorem | Other | easy | 4 m. | Practice a problem by applying the theorem and find the value of AE. |
| 3. | Find the length of PS | Other | easy | 3 m. | Try to find the length of PS in triangle ABC by applying the theorem. |
| 4. | Observe the given figure and answer the question | Other | medium | 4 m. | Understand the given question and answer the following. |
| 5. | Prove the theorem | Other | hard | 5 m. | State and prove the theorem in detail. |
| 6. | Construct a triangle | Other | hard | 5 m. | Practice a problem to construct a triangle when its base, vertical angle and the altitude from the vertex to the base are given. |
| 7. | The angle bisector theorem | Other | medium | 1 m. | Work on the problem to find the answers using Thales theorem or angle bisector theorem. |
Periodic assessments
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Homework I | 00:15:00 | easy | 5 m. | |
| 2. | Homework II | 00:25:00 | easy | 8 m. | |
| 3. | Homework III | 00:25:00 | medium | 8 m. | |
| 4. | Homework IV | 00:25:00 | medium | 8 m. | |
| 5. | Homework V | 00:25:00 | medium | 8 m. | |
| 6. | Homework VI | 00:25:00 | medium | 9 m. | |
| 7. | Revision test I | 00:25:00 | medium | 10 m. | |
| 8. | Revision test II | 00:35:00 | hard | 10 m. | |
| 9. | Revision test III | 00:35:00 | hard | 12 m. | |
| 10. | Revision test IV | 00:35:00 | hard | 14 m. | |
| 11. | Revision test V | 00:35:00 | hard | 16 m. | |
| 12. | Revision test VI | 00:40:00 | hard | 23 m. | |
| 13. | Periodic Assessment | 00:10:00 | medium | 4 m. | PA 1 |
| 14. | Periodic Assessment - 3 | 00:10:00 | medium | 2 m. | PA3 |
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