Page 334 - Start Up Mathematics_7

Proving Pythagoras Theorem by Paper Cutting

Let’s learn a proof of Pythagoras theorem by paper cutting. The credit of discovering this method goes to
London-based stockbroker Henry Perigal.
Procedure

A right-angled triangle ABC and three squares each on one side of D ABC are given on the sheet at the end of
the book (Fig. 1).

• With pencil, draw diagonals of square BCXY lying on side BC. Mark the point of intersection of the
diagonals as O. Then rub off the pencil lines, keeping the point O.

• Draw a line passing through O and parallel to the hypotenuse AB.
• Draw another line passing through O and perpendicular to the previous line. Name the sections thus
formed as II, III, IV and V.
• Cut out square ALMC drawn on side AC. Also cut the pieces II, III, IV and V.
• Now fit these five pieces into square ABQR to prove the Pythagoras theorem.
[Hint: Arrange the square in the centre.]

Making Three-Dimensional Object

• Cut out the net given on the sheet at the end of the book (Fig. 2) along the solid lines.

• Fold it along the dotted lines and paste the flaps to obtain a 3-D object.
On the basis of the object obtained, fill the table given below:

Features Object

1. Name of the figure obtained

2. Number of faces

3. Shape of faces

4. Number of vertices

5. Number of edges

326