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  1. Chapter 11 Class 9 Constructions
  2. Serial order wise
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Construction 11.3 : To construct an angle of 60° at the initial Point of a given ray. Let us take a ray AB with initial Point A. We want to construct a ray AC such that ∠CAB = 60° Steps of Construction : Taking A as centre and some radius, draw an arc of a circle, which intersects AB at Point D. Taking D as Centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point E. Draw the ray AC Passing through E. Thus, ∠CAB is the required angle of 60° Justification We need to prove ∠ CAB = 60° Join DE. Since arc AD = Arc AE and using same radius, we drew arc DE Thus, their radius will be the same ∴ AE = AD = DE    Therefore, ∆ EAD is an equilateral triangle ∴ ∠EAD = 60° ⇒ ∠CAB = 60°. Hence justified

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.