[Class 7] Justify why AB in Fig. 6.4 is the perpendicular bisector - Construction Methods in Śulba-Sūtras

part 2 - Question 1 - Figure it out (Page 142) - Construction Methods in Śulba-Sūtras - Chapter 6 Class 7 - Constructions and Tilings (Ganita Prakash II) - Class 7 (Ganita Prakash 1, 2 & old NCERT)

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Question 1 - Figure it out (Page 142) Justify why AB in Fig. 6.4 is the perpendicular bisectorThink about Symmetry: When you pulled the rope tight to make Point A, the rope length on the left (from 𝑋 to 𝐴 ) was exactly the same as the rope length on the right (from 𝑌 to 𝐴 ). This created a perfectly balanced Triangle (an isosceles triangle). The same thing happened at the bottom for Point B. Because A and B are both perfectly balanced between X and Y , the line connecting them must go straight down the middle! In geometry, the line connecting the tips of two back-to-back isosceles triangles (a kite shape) always crosses the middle at 90^∘. Thus, AB is Mid-point of XY Crosses at 90° ∴ AB is the perpendicular bisector

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