Math Labs with Activity – Pythagoras’ theorem (Method 2)

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Math Labs with Activity – Pythagoras theorem (Method 2)

OBJECTIVE

To verify Pythagoras’ theorem (Method 2)

Materials Required

  1. A piece of cardboard
  2. Two sheets of white paper
  3. A pair of scissors
  4. A geometry box
  5. A tube of glue

Theory
Pythagoras’ theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Procedure
Step 1: Paste a sheet of white paper on the cardboard.
” On this paper, draw a right-angled triangle ABC, right angled at C. Let the lengths of the sides AB, BC and CA be c, a and b units respectively (see Figure 10.1).
Math Labs with Activity - Pythagoras' theorem (Method 2) 1
Step 2: Make four exact copies of the right-angled ΔABC on the other sheet of paper. Also, construct a square with each side measuring c units.
Step 3: Cut these four triangles and the square, arid arrange them as shown in Figure 10.2.
Math Labs with Activity - Pythagoras' theorem (Method 2) 2

Observations and Calculations
We observe that by the combination of the square and the four triangles, a new square is formed which clearly has each side equal to (a+b) units. Then,
area of the large square formed = area of the square with side c + 4 (area of ΔABC)
i.e., (a+b)² =c² +4 (½ x a x b)     [∴ area of ΔABC = ½ (a x b)]
=> (a² + b² + 2ab) =c² + 2ab
=> a² + b² =c².
So, the square of the hypotenuse of right-angled ΔABC is equal to the sum of the squares of the other two sides.

Result
Pythagoras’ theorem is verified.

Remarks:
This method is just a process of verification of Pythagoras’ theorem and cannot be used as a proof for the theorem.

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