Lesson Plan: Trigonometry and Euclidean Geometry (Pythagorean Theorem)

Subject: Mathematics

Class: JSS 2

Term: Second Term

Week: 7

Topic: Trigonometry and Euclidean Geometry – Pythagorean Theorem

Sub-topic: Understanding and Applying the Pythagorean Theorem

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Behavioral Objectives

By the end of the lesson, students should be able to:

1. Define the Pythagorean theorem.
2. Identify the hypotenuse, opposite, and adjacent sides of a right-angled triangle.
3. Apply the Pythagorean theorem to find missing sides of right-angled triangles.
4. Solve real-life problems using the Pythagorean theorem.

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Keywords

• Trigonometry
• Euclidean Geometry
• Pythagorean Theorem
• Hypotenuse
• Right-Angled Triangle
• Opposite Side
• Adjacent Side

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Set Induction (Lesson Introduction)

The teacher draws a right-angled triangle on the board and asks students:
“What do you notice about this triangle? What is special about it?”
After responses, the teacher explains that right-angled triangles follow a special rule known as the Pythagorean Theorem.

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Entry Behavior

Students have prior knowledge of basic triangles and their properties.

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Learning Resources and Materials

• Charts showing right-angled triangles
• Rulers, graph sheets, and protractors
• Mathematics textbooks

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Building Background/Connection to Prior Knowledge

• Students have learned about triangles and their types.
• The teacher links the lesson to real-life applications such as measuring distances and construction.

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Embedded Core Skills

• Numeracy Skills – Applying mathematical rules to solve problems.
• Critical Thinking – Analyzing and solving for unknown sides of a triangle.
• Problem-Solving – Using the Pythagorean theorem in real-life scenarios.

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Learning Materials

• Lagos State Scheme of Work
• Mathematics textbooks (JSS 2)
• Online resources: Khan Academy – Pythagorean Theorem

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Instructional Materials

• Chart showing a right-angled triangle with labeled sides
• Measuring tapes for practical exercises

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Lesson Presentation

Step 1: Introduction to the Pythagorean Theorem

Teacher’s Activity:

• Defines the Pythagorean Theorem as:
  In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
  • Mathematically: c² = a² + b²
• Identifies parts of a right-angled triangle:
  • Hypotenuse (longest side)
  • Opposite (side opposite the given angle)
  • Adjacent (side next to the given angle)

Learner’s Activity:

• Students identify and label parts of a given right-angled triangle.

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Step 2: Applying the Pythagorean Theorem

Teacher’s Activity:

• Provides a worked example:
  • Given a triangle with sides 3 cm and 4 cm, find the hypotenuse.
  • Solution: c² = 3² + 4² = 9 + 16 = 25 → c = √25 = 5 cm

Learner’s Activity:

• Students solve similar problems with teacher guidance.

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Step 3: Solving Word Problems with the Pythagorean Theorem

Teacher’s Activity:

• Gives real-life examples:
  • A ladder is 10 m long and reaches a wall 8 m high. How far is the base of the ladder from the wall?
  • Solution: c² = a² + b²
    • 10² = 8² + b²
    • 100 = 64 + b²
    • b² = 36 → b = √36 = 6 m
  • The base of the ladder is 6 m from the wall.

Learner’s Activity:

• Students practice solving real-world problems using the Pythagorean theorem.

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Evaluation Questions

1. What is the Pythagorean theorem?
   a) a² + b² = c²
   b) a² – b² = c²
   c) a + b = c
   d) a × b = c

2. The hypotenuse is the ____ side of a right-angled triangle.
   a) shortest
   b) longest
   c) equal
   d) opposite

3. In a right-angled triangle, if one side is 6 cm and another is 8 cm, what is the hypotenuse?
   a) 10 cm
   b) 12 cm
   c) 14 cm
   d) 16 cm

4. Solve for the missing side: c² = 9 + 16
   a) 3 cm
   b) 4 cm
   c) 5 cm
   d) 6 cm

5. A ladder is leaning against a wall. If the ladder is 13 m long and the base is 5 m from the wall, what is the height of the wall?
   a) 10 m
   b) 12 m
   c) 15 m
   d) 17 m

6. If a right-angled triangle has sides 5 cm and 12 cm, what is the hypotenuse?
   a) 10 cm
   b) 13 cm
   c) 15 cm
   d) 18 cm

7. What type of triangle does the Pythagorean theorem apply to?
   a) Equilateral triangle
   b) Isosceles triangle
   c) Right-angled triangle
   d) Scalene triangle

8. If the hypotenuse is 25 cm and one side is 24 cm, find the other side.
   a) 7 cm
   b) 9 cm
   c) 11 cm
   d) 15 cm

9. A boat travels 6 km east and 8 km north. How far is it from its starting point?
   a) 10 km
   b) 12 km
   c) 14 km
   d) 16 km

10. What is the value of c in c² = 36 + 64?
    a) 5
    b) 10
    c) 8
    d) 12

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Class Activity Discussion – FAQs

1. What is the Pythagorean theorem?
   It states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

2. How do you find the hypotenuse of a right-angled triangle?
   Use the formula c² = a² + b² and take the square root of the result.

3. Can the Pythagorean theorem be used in all triangles?
   No, it only applies to right-angled triangles.

4. What are some real-life uses of the Pythagorean theorem?
   It is used in navigation, construction, and determining distances.

5. How do I find a missing leg of a right-angled triangle?
   Use b² = c² – a², then find the square root of b².

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Assessment – Short Answer Questions

1. Define the Pythagorean theorem.
2. Find the hypotenuse of a triangle with sides 9 cm and 12 cm.
3. Solve for x if a triangle has sides 7 cm and x cm, with a hypotenuse of 25 cm.
4. A tree is 15 m high and casts a 20 m shadow. How far is the tip of the shadow from the top of the tree?
5. Find the missing side if c = 17 and a = 8.
6. How do you know a triangle is right-angled?
7. Solve: c² = 64 + 144

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Conclusion

The teacher summarizes key points and assigns practice exercises for reinforcement.

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