NCERT Solutions of Chapter: Constructions. NCERT Solutions along with worksheets and notes for Class 9.
Exercise 11.1
(1) Construct an angle of 900 at the initial point of a given ray and justify the construction.
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Given – A ray AB with initial point A.
What to construct – Draw an angle of 900 at initial point A.
Steps of Construction –
(a)Draw a ray AB with A as initial point.
(b) Draw an arc of any radius with A as a centre which intersects AB at point D.
(c) Draw an arc with same radius from point D as centre which intersect previous arc at point E.
(d) Again draw an arc of same radius with centre E which intersects previous arc at point F.
(e) Take radius more than half of the arc EF. Draw two arc from point E and F with radius more than half of EF.
(f) Both arcs intersect at point G.
(g) Join A to G. Draw ray AC passing through G.
Therefore, ∠CAB = = 900
(2)Construct an angle of 450 at the initial point of a giben ray and justify the construction.
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Given – A ray AB with initial point A.
What to construct – Draw an angle of 450 at initial point A.
Steps of Construction –
(a)Draw a ray AB with A as initial point.
(b) Draw an arc of any radius with A as a centre which intersects AB at point D.
(c) Draw an arc with same radius from point D as centre which intersect previous arc at point E.
(d) Again draw an arc of same radius with centre E which intersects previous arc at point F.
(e) Take radius more than half of the arc EF. Draw two arc from point E and F with radius more than half of EF.
(f) Both arcs intersect at point G.
(g) Join A to G. Draw ray AC passing through G.
∠CAB =900
(h) Now, bisect angle CAB.
Take radius more than half of the arc HD. Draw two arcs from point H and D. Arcs intersects at point I.
Join IA. ∠IAB =450.
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(ii)
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or ∠IAB = 75°
(5) Construct an equilateral triangle, given its side and justify the construction.
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Given – One side AB of equilateral triangle ABC.
What to construct – Draw an equilateral triangle ABC.
Steps of construction –
(a)Draw a line AB.
(b)Draw an arc at point A which intersects AB at point D.
(c)Draw another arc from point D with same radius which intersect previous arc at point E.
(d) Join AE. Angle EAB is of measure 600..
(e)Draw an angle of 600 at point B with same procedure.
(f)Let meet both lines at point C.
ABC is required equilateral triangle.
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