Demonstrating Pythagoras' theorem | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these are square numbers?
- 0 ✓
- 1 ✓
- 2
- 4 ✓
- 8
Match each statement to its value.
- 5 squared
  
  ⇔
  
  25 ✓
- the square of 4
  
  ⇔
  
  16 ✓
- 12²
  
  ⇔
  
  144 ✓
- 20 × 20
  
  ⇔
  
  400 ✓
- $\sqrt{4}$
  
  ⇔
  
  2 ✓
- $\sqrt{25}$
  
  ⇔
  
  5 ✓
The difference between 11² and 7² is ______.
- '72' ✓
8² + 6² – 10² = ______.
- '0' ✓
Which of these show a fully and correctly correctly marked square?
- shape A
- shape B
- shape C
- shape D ✓
- shape E
Starting with the smallest, place these angles in order of size.
- 1
  
  ⇔
  
  0°
- 2
  
  ⇔
  
  acute angle
- 3
  
  ⇔
  
  right angle
- 4
  
  ⇔
  
  obtuse angle
- 5
  
  ⇔
  
  reflex angle
- 6
  
  ⇔
  
  angle around a point that makes one full turn

Exit quiz

What is the size of the largest angle in the triangle formed from these three squares?
- acute
- obtuse ✓
- reflex
- right
- impossible to tell
Which of these three angles is the largest?
- $x$ °
- $y$ ° ✓
- $z$ °
- impossible to tell
Which of these are possible sizes for the largest angle?
- 46°
- 68° ✓
- 90°
- 124°
- 173°
If three congruent squares are joined at their vertices, what type of triangle is formed?
- equilateral ✓
- isosceles
- isosceles, right-angled
- scalene
- scalene, right-angled
Two congruent squares, A and B, and a third square, C, are joined at their vertices. The area of square C is less than the area of square A. What type of triangle is formed?
- equilateral
- isosceles ✓
- isosceles, right-angled
- scalene
- scalene, right-angled
A right-angled triangle is formed from three squares. The area of two of the squares are 50 units² and 70 units². What are the possible areas of the third square?
- $7\over5$ units²
- 20 units² ✓
- 65 units²
- 120 units² ✓
- It is impossible for a right-angled triangle to be made from these squares.

Worksheet

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Lesson Details

Key learning points

A visual approach can help you understand the structure behind Pythagoras' theorem.
There is a difference between proof and demonstration.
A demonstration would be showing Pythagoras' theorem works for specific right-angled triangles.
A proof is generalised i.e. using four congruent triangles arranged in a particular way inside a square.
The sum of the squares of the two shorter sides equals the square of the longest side.

Common misconception

Pythagoras' theorem is just a relationship between the three sides of a right-angled triangle.

Whilst this is true, Pythagoras' theorem can more visually be represented as three squares whose sides are equal in length to the three sides of the triangle. The sum of the areas of the two smaller squares is equal to the area of the larger square.

Keywords

Pythagoras' theorem - Pythagoras’ theorem shows that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of its longest side (the hypotenuse).