Question

To verify the Thales theorem by method of paper foldings cutting and pasting.​

Answer 1

Answer:

To verify the Pythagoras theorem by method of Paper Folding, Cutting and Pasting

THEORY:-

Pythagoras theorem:- It states that in a right angled triangle, the square of the largest side (Hypotenuse) is equal to the sum of the squares of the other two sides(Perpendicular and the base).

PRE-REQUISITE KNOWLEDGE:-

Area of a Square

Construction of Parallel lines and Perpendicular bisectors

Construction of a Right triangle

MATERIALS REQUIRED:-

Coloured Paper, A pair of Scissors, Geometry box, Sketch Pens, Fevicol

PROCEDURE:-

1) Cut out a right angled triangle ABC, with sides AC=8cm, AB=10cm, BC=6cm.

2) Cut 3 squares of dimensions 6cm x 6cm, 8cm x 8cm and 10cm x 10cm.

3) Place these squares on the sides of the triangle ABC corresponding to the sides of the square.

4) Now join the the diagonals of the square placed on the perpendicular or the base, say perpendicular.

5) Throught the intersection point of the diagonals draw a line parallel to the base of the Hypotenuse AB of triangle ABC.

6) Now draw perpendicular bisector of the line segment drawn inside the square . Clearly the square is now divided into 4 parts by the former and the latter lines.

7) Now place these 4 quadrilaterals(parts) on the square of dimension corresponding to the hypotenuse such that all the right angles of the quadrilateral coincide with the 4 corners of the large square.

8) Now place the left out square in the middle space left.

OBSERVATION:-

we observe that the squares corresponding to the perpendicular and base of the triangle exactly fit over the square corresponding to the hypotenuse.

RESULT:-

Hence, we conclude that the area of the bigger square is equal to the sum of areas of two smaller squares. Hence, Square of the hypotenuse is equal to the sum of the squares of the other 2 sides of the right angled triangle.

Hence, Pythagoras theorem is verified.

Step-by-step explanation:

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