**Math Labs with Activity – Pythagoras theorem (Method 4)**

**OBJECTIVE**

To verify Pythagoras’ theorem (Method 4)

**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 12.1).

**Step 2:** On the other sheet of paper, draw three squares—one with each side measuring a units, another with each side measuring b units and the third with each side measuring c units. Cut these three squares.

**Step 3:** Place the squares having sides a units and b units together as shown in Figure 12.2.

**Step 4:** Label the diagram as shown in Figure 12.2. Mark a point M on the side GF of the square DEFG such that GM = a units. Join DM and MI. Let MI cut the side EF of the square DEFG at K.

**Step 5:** Separate the two squares. Cut the square DEFG along the lines DM and MK. Cut the square HIJF t along the line KI. Thus, we get two quadrilaterals and three triangles.

**Step 6:** Arrange these two quadrilaterals and three triangles over the square c PQRS with each side measuring c units as shown in Figure 12.3.

**Observations and Calculations**

We observe that the two quadrilaterals and the three triangles can be arranged (as in Figure 12.3) so as to completely cover the square PQRS.

**∴** area of the square PQRS=area of the square HIJF + area of the

square DEFG

i.e., c²=a² + b².

Therefore, the square of the hypotenuse of the right-angled AABC is equal to the sum of the square of the other two sides.

**Result**

Pythagoras’theorem is verified.

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