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Question We have seen how to get 90° using paper folding. Now, suppose we do not have any paper but two sticks of equal length and a thread. How do we make an exact 90° angle using these?
Let AB and CD be two sticks of equal length, say 6 cm. Mark the midpoints of the sticks using a ruler. Fix a screw to the sticks at their midpoints. Using a thread, measure distances AD and BD. Keep on moving the sticks about the screw, so that the distances AD and BD are equal. In this position, fix the sticks by tightening the screw. The new positions of the sticks are shown in the figure. Tie pieces of thread along AD and BD. Consider ∆AMD and ∆BMD. We have AM = BM, AD = BD and MD is common ∴ By the SSS condition, ∆AMD and ∆BMD are congruent. ∴ ∠AMD = ∠BMD Also ∠AMD + ∠BMD = 180° (Linear angles) ∴ ∠AMD + ∠AMD = 180° ⇒ 2∠AMD = 180° ⇒ ∠AMD = 90° ∴ ∠AMD = ∠BMD = 90° ∴ Angle between the sticks is 90°.