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Learning by Doing

Objective: To draw a perpendicular to a line from a point not on it, by paper folding
Materials required: Thick paper, pencil/pen

Procedure:
• Fold the paper from a corner and get a crease, say AB. Mark a point C on the paper that
does not lie on AB, as shown in Fig. 2.

Figure 1 Figure 2

• Through C, fold the paper such that a part of AB falls along AB itself.

Figure 3 Figure 4 Figure 5
• Unfold the sheet. Label the point of intersection of AB and the new line as D.

• Thus, line DC is perpendicular to line AB from C. (Note: You can verify the result by
actual measurement.)

Extension:
1. Repeat this activity taking some more points (other than C) not lying on AB. It can be
seen that there may be infinitely many perpendiculars to a line, but there is only one
perpendicular to a line through a point not on it.
2. Through the same activity, drawing a line parallel to a given line can also be demonstrated.

Knowledge Desk — Mathematician
In the eighth century BCE, the Indian priest Baudhayana was born. Long before Pythagoras was born, he is
credited with creating the concept of the so-called Pythagoras theorem. In his book Sulba Sutra, Baudhayana
provided numerous theorems primarily for the construction of the altar for Yagna. His main contributions
included the Pythagoras theorem, triplets, circling the square, an approximate value of the square root of 2,
bisecting a line segment, and the construction of geometrical shapes such as triangles, squares, rhombuses,
trapeziums, pentagons, and others.

67 Lines and Angles