Pythogoras theorem by Activity|How to prove Pythogoras theoren by Activity

Topic: Pythagoras theorem

Statement: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Objective: To prove the above theorem through activity.

Materials required:

(i) Drawing sheets/poster papers

(ii) Paint box/coloured glazed papers

(iii) Geometry box

(iv) Pair of scissors

(v) Fevistick/gum.

Method 1:

Pre-requisite knowledge: Formula for the area of a square.

To perform the activity:

Steps:

1. Draw any right triangle ABC, right angled at C, on a poster paper and paint it red. Let the lengths of AB, BC and CA be c, a and b units respectively as shown in fig 3.1

2. Construct squares on AB, BC, CA and paint these squares yellow, greet and blue respectively as shown in fig 3.1

3. Make 8 exact copies (replicas) of triangle ABC and paint these red.

4. Take 4 copies of AABC (Painted red) and the green and blue squares. Paste all the figures on drawing sheet as shown in fig 3.2

Take the 4 remaining copies of triangle ABC (painted red) and the yellow square. Paste all these figures on a drawing sheet (as shown in fig. 3.3).

Result:

We observe that each of the figures as shown in fig. 3.2 and 3.3  is a square of side (a + b) units.

Area of square in fig 3.2 = area of square in fig 3.3.

Now remove the four triangles from fig. 3.2 and the four triangles from fig. 3.3.

Since the areas of the triangles removed from both figures is the same, therefore, the remaining areas of both figures are equal

i.e. area of green square + area of blue square = area of yellow square a² + b² = c2

Note: From figure 3.2, we find that:

area of the square with side (a + b) units = area of green square + area of blue square + 4 times area of triangle ABC 

(a+b)²= a² + b² + 4x1/2 x a x b

(a+ b) ² = a²+ b²  + 2ab

 Thus the above model can be used to prove the identity (a + b)² = a² + b² + 2ab for all positive values of a and b.