Introduction to Pythagoras' Theorem
This lesson introduces Year 9 students to Pythagoras' theorem. It covers the identification of parts of a right-angled triangle, the derivation of the formula, and the application of the formula to find missing lengths of both the hypotenuse and shorter sides.
Learning objectives
- Identify the hypotenuse as the longest side of a right-angled triangle, opposite the right angle.
- Calculate the length of the hypotenuse in a right-angled triangle using $a^2 + b^2 = c^2$.
- Rearrange the theorem to calculate the length of a shorter side in a right-angled triangle.
- Apply Pythagoras' theorem to solve simple real-life problems.
Lesson plan (60 minutes)
Starter · 5 min
Do Now: Mental arithmetic and squaring numbers/finding square roots.
Introduction · 10 min
Introduction to Pythagoras' Theorem: History, the formula, and labeling the hypotenuse.
Guided Practice · 10 min
Teacher-led worked examples: Calculating the hypotenuse and then a shorter side.
Independent Practice · 20 min
Differentiated worksheet practice (Support/Core/Stretch).
Assessment · 10 min
Multiple-choice assessment quiz.
Plenary · 5 min
Review answers and self-reflection.
Key vocabulary
- Right-angled triangle
- A triangle containing one angle of 90 degrees.
- Hypotenuse
- The longest side of a right-angled triangle, opposite the right angle.
- Pythagoras' Theorem
- A formula stating that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- Square (a number)
- To multiply a number by itself.
- Square root
- The value that, when multiplied by itself, gives the original number.
Core worksheet (first questions)
- Calculate the hypotenuse for sides 5cm and 8cm (2dp).
- Calculate the hypotenuse for sides 5cm and 5cm (2dp).
- Calculate the hypotenuse for sides 4cm and 12cm (2dp).
- Find the missing side if hypotenuse = 10cm and one side = 6cm.
Quiz (sample)
1. What is the definition of the hypotenuse?
- A. The shortest side
- B. The side opposite the right angle
- C. The vertical side
- D. The side next to the right angle
2. Which formula represents Pythagoras' theorem?
- A. a + b = c
- B. a^2 - b^2 = c^2
- C. a^2 + b^2 = c^2
- D. 2a + 2b = 2c
3. In a right-angled triangle, the two shorter sides are 6cm and 8cm. What is the length of the hypotenuse?
- A. 7cm
- B. 14cm
- C. 10cm
- D. 100cm
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