**Math Labs with Activity – Pythagoras theorem (Method 3)**

**OBJECTIVE**

To verify Pythagoras’ theorem (Method 3)

**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 11.1).

**Step 2:** Make an exact replica of this ΔABC on the other paper.

Construct a square with the side AB as one of its sides. Now, each side of this square is equal to c units.

Similarly, construct two squares with sides measuring a units and b units along the sides and CA of the ΔABC. Label the diagram as shown in Figure 11.2. Also, shade the squares as shown in Figure 11.2.

**Step 3:** Produce the side DA of the square DEBA to meet the side IH of the square ACHI at M. At point M, draw NM perpendicular to AM, so that N lies on the side CH of the square ACHI.

**Step 4:** Produce the side EB of the square DEBA to meet the side CG of the square BFGC at P.

**Step 5:** Cut the squares DEBA, BFGC and ACHI. Also, cut the square BFGC along the line BP and the square ACHI along the lines AM and MN. We thus have a square DEBA, two quadrilaterals—BFGP and ACNM—and three triangles—BCP, AIM and NHM.

**Step 6:** Arrange the two quadrilaterals and the three triangles on the square DEBA as shown in Figure 11.3.

**Observations and Calculations**

We observe that all the parts of the squares BFGC and ACHI, i.e., two quadrilaterals and three triangles completely cover the square DEBA. Therefore,

area of the square DEBA = area of the square BFGC + area of the square ACHI

i.e., c² = a² + b².

In other words, 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 of the theorem.

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