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.

Ans-

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 60^0..

(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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Helping Topics

Constructions

Worksheet Class 9

Practical Geometry