Question 7 of 11intermediate🔧 ApplyShort Answer2 marks

Come up with a method to construct the angle bisector using a rope.

Correct Answer

Step 1: Let ∠XOY be the given angle with vertex O.

Step 2: Take a rope and mark a point A on OX such that the rope length from O to A is convenient.

Step 3: Using the same rope length, mark point B on OY such that OB = OA.

Step 4: Fold the rope in half to find its midpoint.

Step 5: Place one end at A and the other at B, then pull the midpoint away from the angle.

Step 6: Mark this position as C.

Step 7: OC is the angle bisector.

Why it works: AC = BC (midpoint of rope) and OA = OB, making triangles OAC and OBC congruent by SSS.

Exercise: Figure it Out (Section 3) | Q: 5 | (Page Page 9)
For More Understanding

Explanation

The chapter describes rope-based constructions from the Śulba-Sūtras. The principle is the same as compass construction — creating congruent triangles. The rope serves as both a measuring tool (to ensure equal distances) and a marking tool. When the rope is folded in half, its midpoint is equidistant from both ends, which is essential for creating the point C that is equidistant from A and B.

Solution Steps

  1. Let ∠XOY be the given angle with vertex O.

  2. Take a rope and mark a point A on OX such that the rope length from O to A is convenient.

  3. Using the same rope length, mark point B on OY such that OB = OA.

  4. Fold the rope in half to find its midpoint.

  5. Place one end at A and the other at B, then pull the midpoint away from the angle.

  6. Mark this position as C.

  7. OC is the angle bisector.

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