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

**OBJECTIVE**

To verify Pythagoras’ theorem (Method 2)

**Materials Required**

- A piece of cardboard
- Two sheets of white paper
- A pair of scissors
- A geometry box
- 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).

**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.

**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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